econml._cate_estimator
Base classes for all CATE estimators.
Classes
Base class for all CATE estimators in this package. 

Mixin for cate models where the final stage is a debiased lasso model. 

Mixin for cate models where the final stage is a debiased lasso model. 

Base class for all CATE estimators in this package where the outcome is linear given some userdefined treatment featurization. 

Base class for models where the final stage is a linear model. 

Base class for models where the final stage is a linear model. 

Mixin class that offers inference='statsmodels' options to the CATE estimator that inherits it. 

Mixin class that offers inference='statsmodels' options to the CATE estimator that inherits it. 

Mixin which automatically handles promotions of scalar treatments to the appropriate shape, as well as treatment featurization for discrete treatments and userspecified treatment transformers 
 class econml._cate_estimator.BaseCateEstimator[source]
Bases:
object
Base class for all CATE estimators in this package.
 ate(X=None, *, T0, T1)[source]
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)[source]
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)[source]
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)[source]
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)[source]
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)[source]
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 abstract effect(X=None, *, T0, T1)[source]
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)[source]
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)[source]
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)[source]
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 marginal_ate(T, X=None)[source]
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)[source]
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)[source]
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)[source]
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)[source]
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)[source]
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 class econml._cate_estimator.DebiasedLassoCateEstimatorDiscreteMixin[source]
Bases:
econml._cate_estimator.LinearModelFinalCateEstimatorDiscreteMixin
Mixin for cate models where the final stage is a debiased lasso model.
 ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 coef_(T)
The coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
coef – Where n_x is the number of features that enter the final model (either the dimension of X or the dimension of featurizer.fit_transform(X) if the CATE estimator has a featurizer.)
 Return type
(n_x,) or (n_y, n_x) array_like
 coef__inference(T)
The inference for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
InferenceResults – The inference of the coefficients in the final linear model
 Return type
 coef__interval(T, *, alpha=0.05)
The confidence interval for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval for each quantity.
 Return type
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 intercept_(T)
The intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
intercept
 Return type
float or (n_y,) array_like
 intercept__inference(T)
The inference of the intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
InferenceResults – The inference of the intercept in the final linear model
 Return type
 intercept__interval(T, *, alpha=0.05)
The intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval.
 Return type
tuple(type of
intercept_(T)
, type ofintercept_(T)
)
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 summary(T, *, alpha=0.05, value=0, decimals=3, feature_names=None, treatment_names=None, output_names=None)
The summary of coefficient and intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.
decimals (int, default 3) – Number of decimal places to round each column to.
feature_names (list of str, optional) – The input of the feature names
treatment_names (list of str, optional) – The names of the treatments
output_names (list of str, optional) – The names of the outputs
 Returns
smry – this holds the summary tables and text, which can be printed or converted to various output formats.
 Return type
Summary instance
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 class econml._cate_estimator.DebiasedLassoCateEstimatorMixin[source]
Bases:
econml._cate_estimator.LinearModelFinalCateEstimatorMixin
Mixin for cate models where the final stage is a debiased lasso model.
 ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 coef__inference()
The inference of coefficients in the linear model of the constant marginal treatment effect.
 Returns
InferenceResults – The inference of the coefficients in the final linear model
 Return type
 coef__interval(*, alpha=0.05)
The coefficients in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lb, ub – The lower and upper bounds of the confidence interval for each quantity.
 Return type
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 intercept__inference()
The inference of intercept in the linear model of the constant marginal treatment effect.
 Returns
InferenceResults – The inference of the intercept in the final linear model
 Return type
 intercept__interval(*, alpha=0.05)
The intercept in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval.
 Return type
tuple(type of
intercept_()
, type ofintercept_()
)
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 shap_values(X, *, feature_names=None, treatment_names=None, output_names=None, background_samples=100)
Shap value for the final stage models (const_marginal_effect)
 Parameters
X ((m, d_x) matrix) – Features for each sample. Should be in the same shape of fitted X in final stage.
feature_names (list of str of length X.shape[1], optional) – The names of input features.
treatment_names (list, optional) – The name of featurized treatment. In discrete treatment scenario, the name should not include the name of the baseline treatment (i.e. the control treatment, which by default is the alphabetically smaller)
output_names (list, optional) – The name of the outcome.
background_samples (int , default 100) – How many samples to use to compute the baseline effect. If None then all samples are used.
 Returns
shap_outs – A nested dictionary by using each output name (e.g. ‘Y0’, ‘Y1’, … when output_names=None) and each treatment name (e.g. ‘T0’, ‘T1’, … when treatment_names=None) as key and the shap_values explanation object as value. If the input data at fit time also contain metadata, (e.g. are pandas DataFrames), then the column metatdata for the treatments, outcomes and features are used instead of the above defaults (unless the user overrides with explicitly passing the corresponding names).
 Return type
nested dictionary of Explanation object
 summary(alpha=0.05, value=0, decimals=3, feature_names=None, treatment_names=None, output_names=None)
The summary of coefficient and intercept in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.
decimals (int, default 3) – Number of decimal places to round each column to.
feature_names (list of str, optional) – The input of the feature names
treatment_names (list of str, optional) – The names of the treatments
output_names (list of str, optional) – The names of the outputs
 Returns
smry – this holds the summary tables and text, which can be printed or converted to various output formats.
 Return type
Summary instance
 property coef_
The coefficients in the linear model of the constant marginal treatment effect.
 Returns
coef – Where n_x is the number of features that enter the final model (either the dimension of X or the dimension of featurizer.fit_transform(X) if the CATE estimator has a featurizer.), n_t is the number of treatments, n_y is the number of outcomes. Dimensions are omitted if the original input was a vector and not a 2D array. For binary treatment the n_t dimension is also omitted.
 Return type
(n_x,) or (n_t, n_x) or (n_y, n_t, n_x) array_like
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 property intercept_
The intercept in the linear model of the constant marginal treatment effect.
 Returns
intercept – Where n_t is the number of treatments, n_y is the number of outcomes. Dimensions are omitted if the original input was a vector and not a 2D array. For binary treatment the n_t dimension is also omitted.
 Return type
float or (n_y,) or (n_y, n_t) array_like
 class econml._cate_estimator.ForestModelFinalCateEstimatorDiscreteMixin[source]
Bases:
econml._cate_estimator.BaseCateEstimator
 ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 class econml._cate_estimator.ForestModelFinalCateEstimatorMixin[source]
Bases:
econml._cate_estimator.BaseCateEstimator
 ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 class econml._cate_estimator.LinearCateEstimator[source]
Bases:
econml._cate_estimator.BaseCateEstimator
Base class for all CATE estimators in this package where the outcome is linear given some userdefined treatment featurization.
 ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 const_marginal_ate(X=None)[source]
Calculate the average constant marginal CATE \(E_X[\theta(X)]\).
 Parameters
X ((m, d_x) matrix, optional) – Features for each sample.
 Returns
theta – Average constant marginal CATE of each treatment on each outcome. Note that when Y or featurizedT (or T if treatment_featurizer is None) is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a scalar)
 Return type
(d_y, d_f_t) matrix where d_f_t is the dimension of the featurized treatment. If treatment_featurizer is None, d_f_t = d_t.
 const_marginal_ate_inference(X=None)[source]
Inference results for the quantities \(E_X[\theta(X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 const_marginal_ate_interval(X=None, *, alpha=0.05)[source]
Confidence intervals for the quantities \(E_X[\theta(X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
const_marginal_ate(X)
, type ofconst_marginal_ate(X)
)
 abstract const_marginal_effect(X=None)[source]
Calculate the constant marginal CATE \(\theta(·)\).
The marginal effect is conditional on a vector of features on a set of m test samples X[i].
 Parameters
X ((m, d_x) matrix, optional) – Features for each sample.
 Returns
theta – Constant marginal CATE of each featurized treatment on each outcome for each sample X[i]. Note that when Y or featurizedT (or T if treatment_featurizer is None) is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_f_t) matrix or (d_y, d_f_t) matrix if X is None where d_f_t is the dimension of the featurized treatment. If treatment_featurizer is None, d_f_t = d_t.
 const_marginal_effect_inference(X=None)[source]
Inference results for the quantities \(\theta(X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 const_marginal_effect_interval(X=None, *, alpha=0.05)[source]
Confidence intervals for the quantities \(\theta(X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
const_marginal_effect(X)
, type ofconst_marginal_effect(X)
)
 effect(X=None, *, T0, T1)[source]
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\). Since this class assumes a linear effect, only the difference between T0ᵢ and T1ᵢ matters for this computation.
 Parameters
T0 ((m, d_t) matrix) – Base treatments for each sample
T1 ((m, d_t) matrix) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
effect – Heterogeneous treatment effects on each outcome for each sample. Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix (or length m vector if Y was a vector)
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 marginal_ate(T, X=None)[source]
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)[source]
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)[source]
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 marginal_effect(T, X=None)[source]
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\). If treatment_featurizer is None, the base treatment is ignored in this calculation and the result is equivalent to const_marginal_effect.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)[source]
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)[source]
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 shap_values(X, *, feature_names=None, treatment_names=None, output_names=None, background_samples=100)[source]
Shap value for the final stage models (const_marginal_effect)
 Parameters
X ((m, d_x) matrix) – Features for each sample. Should be in the same shape of fitted X in final stage.
feature_names (list of str of length X.shape[1], optional) – The names of input features.
treatment_names (list, optional) – The name of featurized treatment. In discrete treatment scenario, the name should not include the name of the baseline treatment (i.e. the control treatment, which by default is the alphabetically smaller)
output_names (list, optional) – The name of the outcome.
background_samples (int , default 100) – How many samples to use to compute the baseline effect. If None then all samples are used.
 Returns
shap_outs – A nested dictionary by using each output name (e.g. ‘Y0’, ‘Y1’, … when output_names=None) and each treatment name (e.g. ‘T0’, ‘T1’, … when treatment_names=None) as key and the shap_values explanation object as value. If the input data at fit time also contain metadata, (e.g. are pandas DataFrames), then the column metatdata for the treatments, outcomes and features are used instead of the above defaults (unless the user overrides with explicitly passing the corresponding names).
 Return type
nested dictionary of Explanation object
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 class econml._cate_estimator.LinearModelFinalCateEstimatorDiscreteMixin[source]
Bases:
econml._cate_estimator.BaseCateEstimator
Base class for models where the final stage is a linear model.
Subclasses must expose a
fitted_models_final
attribute returning an array of the fitted models for each noncontrol treatment ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 coef_(T)[source]
The coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
coef – Where n_x is the number of features that enter the final model (either the dimension of X or the dimension of featurizer.fit_transform(X) if the CATE estimator has a featurizer.)
 Return type
(n_x,) or (n_y, n_x) array_like
 coef__inference(T)[source]
The inference for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
InferenceResults – The inference of the coefficients in the final linear model
 Return type
 coef__interval(T, *, alpha=0.05)[source]
The confidence interval for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval for each quantity.
 Return type
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 intercept_(T)[source]
The intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
intercept
 Return type
float or (n_y,) array_like
 intercept__inference(T)[source]
The inference of the intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
InferenceResults – The inference of the intercept in the final linear model
 Return type
 intercept__interval(T, *, alpha=0.05)[source]
The intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval.
 Return type
tuple(type of
intercept_(T)
, type ofintercept_(T)
)
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 summary(T, *, alpha=0.05, value=0, decimals=3, feature_names=None, treatment_names=None, output_names=None)[source]
The summary of coefficient and intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.
decimals (int, default 3) – Number of decimal places to round each column to.
feature_names (list of str, optional) – The input of the feature names
treatment_names (list of str, optional) – The names of the treatments
output_names (list of str, optional) – The names of the outputs
 Returns
smry – this holds the summary tables and text, which can be printed or converted to various output formats.
 Return type
Summary instance
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 class econml._cate_estimator.LinearModelFinalCateEstimatorMixin[source]
Bases:
econml._cate_estimator.BaseCateEstimator
Base class for models where the final stage is a linear model.
Such an estimator must implement a
model_final_
attribute that points to the fitted finalStatsModelsLinearRegression
object that represents the fitted CATE model. Also must implementfeaturizer_
that points to the fitted featurizer andbias_part_of_coef
that designates if the intercept is the first element of themodel_final_
coefficient. bias_part_of_coef
Whether the CATE model’s intercept is contained in the final model’s
coef_
rather than as a separateintercept_
 Type
 ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 coef__inference()[source]
The inference of coefficients in the linear model of the constant marginal treatment effect.
 Returns
InferenceResults – The inference of the coefficients in the final linear model
 Return type
 coef__interval(*, alpha=0.05)[source]
The coefficients in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lb, ub – The lower and upper bounds of the confidence interval for each quantity.
 Return type
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 intercept__inference()[source]
The inference of intercept in the linear model of the constant marginal treatment effect.
 Returns
InferenceResults – The inference of the intercept in the final linear model
 Return type
 intercept__interval(*, alpha=0.05)[source]
The intercept in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval.
 Return type
tuple(type of
intercept_()
, type ofintercept_()
)
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 shap_values(X, *, feature_names=None, treatment_names=None, output_names=None, background_samples=100)[source]
Shap value for the final stage models (const_marginal_effect)
 Parameters
X ((m, d_x) matrix) – Features for each sample. Should be in the same shape of fitted X in final stage.
feature_names (list of str of length X.shape[1], optional) – The names of input features.
treatment_names (list, optional) – The name of featurized treatment. In discrete treatment scenario, the name should not include the name of the baseline treatment (i.e. the control treatment, which by default is the alphabetically smaller)
output_names (list, optional) – The name of the outcome.
background_samples (int , default 100) – How many samples to use to compute the baseline effect. If None then all samples are used.
 Returns
shap_outs – A nested dictionary by using each output name (e.g. ‘Y0’, ‘Y1’, … when output_names=None) and each treatment name (e.g. ‘T0’, ‘T1’, … when treatment_names=None) as key and the shap_values explanation object as value. If the input data at fit time also contain metadata, (e.g. are pandas DataFrames), then the column metatdata for the treatments, outcomes and features are used instead of the above defaults (unless the user overrides with explicitly passing the corresponding names).
 Return type
nested dictionary of Explanation object
 summary(alpha=0.05, value=0, decimals=3, feature_names=None, treatment_names=None, output_names=None)[source]
The summary of coefficient and intercept in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.
decimals (int, default 3) – Number of decimal places to round each column to.
feature_names (list of str, optional) – The input of the feature names
treatment_names (list of str, optional) – The names of the treatments
output_names (list of str, optional) – The names of the outputs
 Returns
smry – this holds the summary tables and text, which can be printed or converted to various output formats.
 Return type
Summary instance
 property coef_
The coefficients in the linear model of the constant marginal treatment effect.
 Returns
coef – Where n_x is the number of features that enter the final model (either the dimension of X or the dimension of featurizer.fit_transform(X) if the CATE estimator has a featurizer.), n_t is the number of treatments, n_y is the number of outcomes. Dimensions are omitted if the original input was a vector and not a 2D array. For binary treatment the n_t dimension is also omitted.
 Return type
(n_x,) or (n_t, n_x) or (n_y, n_t, n_x) array_like
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 property intercept_
The intercept in the linear model of the constant marginal treatment effect.
 Returns
intercept – Where n_t is the number of treatments, n_y is the number of outcomes. Dimensions are omitted if the original input was a vector and not a 2D array. For binary treatment the n_t dimension is also omitted.
 Return type
float or (n_y,) or (n_y, n_t) array_like
 class econml._cate_estimator.StatsModelsCateEstimatorDiscreteMixin[source]
Bases:
econml._cate_estimator.LinearModelFinalCateEstimatorDiscreteMixin
Mixin class that offers inference=’statsmodels’ options to the CATE estimator that inherits it.
Such an estimator must implement a
model_final_
attribute that points to aStatsModelsLinearRegression
object that is cloned to fit each discrete treatment target CATE model and afitted_models_final
attribute that returns the list of fitted final models that represent the CATE for each categorical treatment. ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 coef_(T)
The coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
coef – Where n_x is the number of features that enter the final model (either the dimension of X or the dimension of featurizer.fit_transform(X) if the CATE estimator has a featurizer.)
 Return type
(n_x,) or (n_y, n_x) array_like
 coef__inference(T)
The inference for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
InferenceResults – The inference of the coefficients in the final linear model
 Return type
 coef__interval(T, *, alpha=0.05)
The confidence interval for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval for each quantity.
 Return type
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 intercept_(T)
The intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
intercept
 Return type
float or (n_y,) array_like
 intercept__inference(T)
The inference of the intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
 Returns
InferenceResults – The inference of the intercept in the final linear model
 Return type
 intercept__interval(T, *, alpha=0.05)
The intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
T (alphanumeric) – The input treatment for which we want the coefficients.
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval.
 Return type
tuple(type of
intercept_(T)
, type ofintercept_(T)
)
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 summary(T, *, alpha=0.05, value=0, decimals=3, feature_names=None, treatment_names=None, output_names=None)
The summary of coefficient and intercept in the linear model of the constant marginal treatment effect associated with treatment T.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.
decimals (int, default 3) – Number of decimal places to round each column to.
feature_names (list of str, optional) – The input of the feature names
treatment_names (list of str, optional) – The names of the treatments
output_names (list of str, optional) – The names of the outputs
 Returns
smry – this holds the summary tables and text, which can be printed or converted to various output formats.
 Return type
Summary instance
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 class econml._cate_estimator.StatsModelsCateEstimatorMixin[source]
Bases:
econml._cate_estimator.LinearModelFinalCateEstimatorMixin
Mixin class that offers inference=’statsmodels’ options to the CATE estimator that inherits it.
Such an estimator must implement a
model_final_
attribute that points to the fitted finalStatsModelsLinearRegression
object that represents the fitted CATE model. Also must implementfeaturizer_
that points to the fitted featurizer andbias_part_of_coef
that designates if the intercept is the first element of themodel_final_
coefficient. ate(X=None, *, T0, T1)
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0, T1)
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0, T1, alpha=0.05)
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)
Public interface for getting treatment names.
To be overriden by estimators that apply transformations the treatments.
 Parameters
treatment_names (list of str of length T.shape[1] or None) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
treatment_names – Returns treatment names.
 Return type
list of str
 coef__inference()
The inference of coefficients in the linear model of the constant marginal treatment effect.
 Returns
InferenceResults – The inference of the coefficients in the final linear model
 Return type
 coef__interval(*, alpha=0.05)
The coefficients in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lb, ub – The lower and upper bounds of the confidence interval for each quantity.
 Return type
 abstract effect(X=None, *, T0, T1)
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 intercept__inference()
The inference of intercept in the linear model of the constant marginal treatment effect.
 Returns
InferenceResults – The inference of the intercept in the final linear model
 Return type
 intercept__interval(*, alpha=0.05)
The intercept in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and upper bounds of the confidence interval.
 Return type
tuple(type of
intercept_()
, type ofintercept_()
)
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 shap_values(X, *, feature_names=None, treatment_names=None, output_names=None, background_samples=100)
Shap value for the final stage models (const_marginal_effect)
 Parameters
X ((m, d_x) matrix) – Features for each sample. Should be in the same shape of fitted X in final stage.
feature_names (list of str of length X.shape[1], optional) – The names of input features.
treatment_names (list, optional) – The name of featurized treatment. In discrete treatment scenario, the name should not include the name of the baseline treatment (i.e. the control treatment, which by default is the alphabetically smaller)
output_names (list, optional) – The name of the outcome.
background_samples (int , default 100) – How many samples to use to compute the baseline effect. If None then all samples are used.
 Returns
shap_outs – A nested dictionary by using each output name (e.g. ‘Y0’, ‘Y1’, … when output_names=None) and each treatment name (e.g. ‘T0’, ‘T1’, … when treatment_names=None) as key and the shap_values explanation object as value. If the input data at fit time also contain metadata, (e.g. are pandas DataFrames), then the column metatdata for the treatments, outcomes and features are used instead of the above defaults (unless the user overrides with explicitly passing the corresponding names).
 Return type
nested dictionary of Explanation object
 summary(alpha=0.05, value=0, decimals=3, feature_names=None, treatment_names=None, output_names=None)
The summary of coefficient and intercept in the linear model of the constant marginal treatment effect.
 Parameters
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.
decimals (int, default 3) – Number of decimal places to round each column to.
feature_names (list of str, optional) – The input of the feature names
treatment_names (list of str, optional) – The names of the treatments
output_names (list of str, optional) – The names of the outputs
 Returns
smry – this holds the summary tables and text, which can be printed or converted to various output formats.
 Return type
Summary instance
 property coef_
The coefficients in the linear model of the constant marginal treatment effect.
 Returns
coef – Where n_x is the number of features that enter the final model (either the dimension of X or the dimension of featurizer.fit_transform(X) if the CATE estimator has a featurizer.), n_t is the number of treatments, n_y is the number of outcomes. Dimensions are omitted if the original input was a vector and not a 2D array. For binary treatment the n_t dimension is also omitted.
 Return type
(n_x,) or (n_t, n_x) or (n_y, n_t, n_x) array_like
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance
 property intercept_
The intercept in the linear model of the constant marginal treatment effect.
 Returns
intercept – Where n_t is the number of treatments, n_y is the number of outcomes. Dimensions are omitted if the original input was a vector and not a 2D array. For binary treatment the n_t dimension is also omitted.
 Return type
float or (n_y,) or (n_y, n_t) array_like
 class econml._cate_estimator.TreatmentExpansionMixin[source]
Bases:
econml._cate_estimator.BaseCateEstimator
Mixin which automatically handles promotions of scalar treatments to the appropriate shape, as well as treatment featurization for discrete treatments and userspecified treatment transformers
 ate(X=None, *, T0=0, T1=1)[source]
Calculate the average treatment effect \(E_X[\tau(X, T0, T1)]\).
The effect is calculated between the two treatment points and is averaged over the population of X variables.
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Average treatment effects on each outcome Note that when Y is a vector rather than a 2dimensional array, the result will be a scalar
 Return type
float or (d_y,) array
 ate_inference(X=None, *, T0=0, T1=1)[source]
Inference results for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 ate_interval(X=None, *, T0=0, T1=1, alpha=0.05)[source]
Confidence intervals for the quantity \(E_X[\tau(X, T0, T1)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
ate(X, T0, T1)
, type ofate(X, T0, T1))
)
 cate_feature_names(feature_names=None)
Public interface for getting feature names.
To be overriden by estimators that apply transformations the input features.
 Parameters
feature_names (list of str of length X.shape[1] or None) – The names of the input features. If None and X is a dataframe, it defaults to the column names from the dataframe.
 Returns
out_feature_names – Returns feature names.
 Return type
list of str or None
 cate_output_names(output_names=None)
Public interface for getting output names.
To be overriden by estimators that apply transformations the outputs.
 Parameters
output_names (list of str of length Y.shape[1] or None) – The names of the outcomes. If None and the Y passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
output_names – Returns output names.
 Return type
list of str
 cate_treatment_names(treatment_names=None)[source]
Get treatment names.
If the treatment is discrete or featurized, it will return expanded treatment names.
 Parameters
treatment_names (list of str of length T.shape[1], optional) – The names of the treatments. If None and the T passed to fit was a dataframe, it defaults to the column names from the dataframe.
 Returns
out_treatment_names – Returns (possibly expanded) treatment names.
 Return type
list of str
 effect(X=None, *, T0=0, T1=1)[source]
Calculate the heterogeneous treatment effect \(\tau(X, T0, T1)\).
The effect is calculated between the two treatment points conditional on a vector of features on a set of m test samples \(\{T0_i, T1_i, X_i\}\).
 Parameters
T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m) – Target treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
τ – Heterogeneous treatment effects on each outcome for each sample Note that when Y is a vector rather than a 2dimensional array, the corresponding singleton dimension will be collapsed (so this method will return a vector)
 Return type
(m, d_y) matrix
 effect_inference(X=None, *, T0=0, T1=1)
Inference results for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 effect_interval(X=None, *, T0=0, T1=1, alpha=0.05)
Confidence intervals for the quantities \(\tau(X, T0, T1)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
X ((m, d_x) matrix, optional) – Features for each sample
T0 ((m, d_t) matrix or vector of length m, default 0) – Base treatments for each sample
T1 ((m, d_t) matrix or vector of length m, default 1) – Target treatments for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
effect(X, T0, T1)
, type ofeffect(X, T0, T1))
)
 abstract fit(*args, inference=None, **kwargs)
Estimate the counterfactual model from data, i.e. estimates functions \(\tau(X, T0, T1)\), \(\partial \tau(T, X)\).
Note that the signature of this method may vary in subclasses (e.g. classes that don’t support instruments will not allow a Z argument)
 Parameters
Y ((n, d_y) matrix or vector of length n) – Outcomes for each sample
T ((n, d_t) matrix or vector of length n) – Treatments for each sample
X ((n, d_x) matrix, optional) – Features for each sample
W ((n, d_w) matrix, optional) – Controls for each sample
Z ((n, d_z) matrix, optional) – Instruments for each sample
inference (str or
Inference
instance, optional) – Method for performing inference. All estimators support'bootstrap'
(or an instance ofBootstrapInference
), some support other methods as well.
 Return type
self
 marginal_ate(T, X=None)
Calculate the average marginal effect \(E_{T, X}[\partial\tau(T, X)]\).
The marginal effect is calculated around a base treatment point and averaged over the population of X.
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Average marginal effects on each outcome Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will be a scalar)
 Return type
(d_y, d_t) array
 marginal_ate_inference(T, X=None)
Inference results for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
PopulationSummaryResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_ate_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(E_{T,X}[\partial \tau(T, X)]\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_ate(T, X)
, type ofmarginal_ate(T, X)
)
 abstract marginal_effect(T, X=None)
Calculate the heterogeneous marginal effect \(\partial\tau(T, X)\).
The marginal effect is calculated around a base treatment point conditional on a vector of features on a set of m test samples \(\{T_i, X_i\}\).
 Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
grad_tau – Heterogeneous marginal effects on each outcome for each sample Note that when Y or T is a vector rather than a 2dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)
 Return type
(m, d_y, d_t) array
 marginal_effect_inference(T, X=None)
Inference results for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
 Returns
InferenceResults – The inference results instance contains prediction and prediction standard error and can on demand calculate confidence interval, z statistic and p value. It can also output a dataframe summary of these inference results.
 Return type
 marginal_effect_interval(T, X=None, *, alpha=0.05)
Confidence intervals for the quantities \(\partial \tau(T, X)\) produced by the model. Available only when
inference
is notNone
, when calling the fit method. Parameters
T ((m, d_t) matrix) – Base treatments for each sample
X ((m, d_x) matrix, optional) – Features for each sample
alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1alpha/2 confidence interval is reported.
 Returns
lower, upper – The lower and the upper bounds of the confidence interval for each quantity.
 Return type
tuple(type of
marginal_effect(T, X)
, type ofmarginal_effect(T, X)
)
 property dowhy
Get an instance of
DoWhyWrapper
to allow other functionalities from dowhy package. (e.g. causal graph, refutation test, etc.) Returns
DoWhyWrapper – An instance of
DoWhyWrapper
 Return type
instance