# econml.dml.DML

class econml.dml.DML(*, model_y, model_t, model_final, featurizer=None, treatment_featurizer=None, fit_cate_intercept=True, linear_first_stages='deprecated', discrete_treatment=False, categories='auto', cv=2, mc_iters=None, mc_agg='mean', random_state=None, allow_missing=False, use_ray=False, ray_remote_func_options=None)[source]

Bases: econml._cate_estimator.LinearModelFinalCateEstimatorMixin, econml.dml.dml._BaseDML

The base class for parametric Double ML estimators. The estimator is a special case of an _RLearner estimator, which in turn is a special case of an _OrthoLearner estimator, so it follows the two stage process, where a set of nuisance functions are estimated in the first stage in a crossfitting manner and a final stage estimates the CATE model. See the documentation of _OrthoLearner for a description of this two stage process.

In this estimator, the CATE is estimated by using the following estimating equations:

$Y - \E[Y | X, W] = \Theta(X) \cdot (T - \E[T | X, W]) + \epsilon$

Thus if we estimate the nuisance functions $$q(X, W) = \E[Y | X, W]$$ and $$f(X, W)=\E[T | X, W]$$ in the first stage, we can estimate the final stage cate for each treatment t, by running a regression, minimizing the residual on residual square loss:

$\hat{\theta} = \arg\min_{\Theta} \E_n\left[ (\tilde{Y} - \Theta(X) \cdot \tilde{T})^2 \right]$

Where $$\tilde{Y}=Y - \E[Y | X, W]$$ and $$\tilde{T}=T-\E[T | X, W]$$ denotes the residual outcome and residual treatment.

The DML estimator further assumes a linear parametric form for the cate, i.e. for each outcome $$i$$ and treatment $$j$$:

$\Theta_{i, j}(X) = \phi(X)' \cdot \Theta_{ij}$

For some given feature mapping $$\phi(X)$$ (the user can provide this featurizer via the featurizer parameter at init time and could be any arbitrary class that adheres to the scikit-learn transformer interface TransformerMixin).

The second nuisance function $$q$$ is a simple regression problem and the DML class takes as input the parameter model_y, which is an arbitrary scikit-learn regressor that is internally used to solve this regression problem.

The problem of estimating the nuisance function $$f$$ is also a regression problem and the DML class takes as input the parameter model_t, which is an arbitrary scikit-learn regressor that is internally used to solve this regression problem. If the init flag discrete_treatment is set to True, then the parameter model_t is treated as a scikit-learn classifier. The input categorical treatment is one-hot encoded (excluding the lexicographically smallest treatment which is used as the baseline) and the predict_proba method of the model_t classifier is used to residualize the one-hot encoded treatment.

The final stage is (potentially multi-task) linear regression problem with outcomes the labels $$\tilde{Y}$$ and regressors the composite features $$\tilde{T}\otimes \phi(X) = \mathtt{vec}(\tilde{T}\cdot \phi(X)^T)$$. The DML takes as input parameter model_final, which is any linear scikit-learn regressor that is internally used to solve this (multi-task) linear regresion problem.

Parameters
• model_y (estimator or ‘auto’, default ‘auto’) – The estimator for fitting the response to the features. Must implement fit and predict methods. If ‘auto’ WeightedLassoCV/WeightedMultiTaskLassoCV will be chosen.

• model_t (estimator or ‘auto’ (default is ‘auto’)) – The estimator for fitting the treatment to the features. If estimator, it must implement fit and predict methods. Must be a linear model for correctness when linear_first_stages is True; If ‘auto’, LogisticRegressionCV will be applied for discrete treatment, and WeightedLassoCV/ WeightedMultiTaskLassoCV will be applied for continuous treatment.

• model_final (estimator) – The estimator for fitting the response residuals to the treatment residuals. Must implement fit and predict methods, and must be a linear model for correctness.

• featurizer (transformer, optional) – Must support fit_transform and transform. Used to create composite features in the final CATE regression. It is ignored if X is None. The final CATE will be trained on the outcome of featurizer.fit_transform(X). If featurizer=None, then CATE is trained on X.

• treatment_featurizer (transformer, optional) – Must support fit_transform and transform. Used to create composite treatment in the final CATE regression. The final CATE will be trained on the outcome of featurizer.fit_transform(T). If featurizer=None, then CATE is trained on T.

• fit_cate_intercept (bool, default True) – Whether the linear CATE model should have a constant term.

• linear_first_stages (bool) – Whether the first stage models are linear (in which case we will expand the features passed to model_y accordingly)

• discrete_treatment (bool, default False) – Whether the treatment values should be treated as categorical, rather than continuous, quantities

• categories (‘auto’ or list, default ‘auto’) – The categories to use when encoding discrete treatments (or ‘auto’ to use the unique sorted values). The first category will be treated as the control treatment.

• verbose (int, default 2) – The verbosity level of the output messages. Higher values indicate more verbosity.

• cv (int, cross-validation generator or an iterable, default 2) – Determines the cross-validation splitting strategy. Possible inputs for cv are:

• None, to use the default 3-fold cross-validation,

• integer, to specify the number of folds.

• CV splitter

• An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, if the treatment is discrete StratifiedKFold is used, else, KFold is used (with a random shuffle in either case).

Unless an iterable is used, we call split(concat[W, X], T) to generate the splits. If all W, X are None, then we call split(ones((T.shape, 1)), T).

• mc_iters (int, optional) – The number of times to rerun the first stage models to reduce the variance of the nuisances.

• mc_agg ({‘mean’, ‘median’}, default ‘mean’) – How to aggregate the nuisance value for each sample across the mc_iters monte carlo iterations of cross-fitting.

• random_state (int, RandomState instance, or None, default None) – If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

• allow_missing (bool) – Whether to allow missing values in X, W. If True, will need to supply model_y, model_t, and model_final that can handle missing values.

• use_ray (bool, default False) – Whether to use Ray to parallelize the cross-validation step. If True, Ray must be installed.

• ray_remote_func_options (dict, default None) – Options to pass to the remote function when using Ray. See https://docs.ray.io/en/latest/ray-core/api/doc/ray.remote.html

Examples

A simple example with discrete treatment and a linear model_final (equivalent to LinearDML):

from econml.dml import DML
from econml.sklearn_extensions.linear_model import StatsModelsLinearRegression
from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier

np.random.seed(123)
X = np.random.normal(size=(1000, 5))
T = np.random.binomial(1, scipy.special.expit(X[:, 0]))
y = (1 + .5*X[:, 0]) * T + X[:, 0] + np.random.normal(size=(1000,))
est = DML(
model_y=RandomForestRegressor(),
model_t=RandomForestClassifier(),
model_final=StatsModelsLinearRegression(fit_intercept=False),
linear_first_stages=False,
discrete_treatment=True
)
est.fit(y, T, X=X, W=None)

>>> est.effect(X[:3])
array([0.65142..., 1.82917..., 0.79287...])
>>> est.effect_interval(X[:3])
(array([0.28936..., 1.31239..., 0.47626...]),
array([1.01348..., 2.34594..., 1.10949...]))
>>> est.coef_
array([ 0.32570..., -0.05311..., -0.03973...,  0.01598..., -0.11045...])
>>> est.coef__interval()
(array([ 0.13791..., -0.20081..., -0.17941..., -0.12073..., -0.25769...]),
array([0.51348..., 0.09458..., 0.09993..., 0.15269..., 0.03679...]))
>>> est.intercept_
1.02940...
>>> est.intercept__interval()
(0.88754..., 1.17125...)

__init__(*, model_y, model_t, model_final, featurizer=None, treatment_featurizer=None, fit_cate_intercept=True, linear_first_stages='deprecated', discrete_treatment=False, categories='auto', cv=2, mc_iters=None, mc_agg='mean', random_state=None, allow_missing=False, use_ray=False, ray_remote_func_options=None)[source]

Methods

 __init__(*, model_y, model_t, model_final[, ...]) ate([X, T0, T1]) Calculate the average treatment effect $$E_X[\tau(X, T0, T1)]$$. ate_inference([X, T0, T1]) Inference results for the quantity $$E_X[\tau(X, T0, T1)]$$ produced by the model. ate_interval([X, T0, T1, alpha]) Confidence intervals for the quantity $$E_X[\tau(X, T0, T1)]$$ produced by the model. cate_feature_names([feature_names]) Get the output feature names. cate_output_names([output_names]) Public interface for getting output names. cate_treatment_names([treatment_names]) Get treatment names. The inference of coefficients in the linear model of the constant marginal treatment effect. coef__interval(*[, alpha]) The coefficients in the linear model of the constant marginal treatment effect. Calculate the average constant marginal CATE $$E_X[\theta(X)]$$. Inference results for the quantities $$E_X[\theta(X)]$$ produced by the model. const_marginal_ate_interval([X, alpha]) Confidence intervals for the quantities $$E_X[\theta(X)]$$ produced by the model. Calculate the constant marginal CATE $$\theta(·)$$. Inference results for the quantities $$\theta(X)$$ produced by the model. const_marginal_effect_interval([X, alpha]) Confidence intervals for the quantities $$\theta(X)$$ produced by the model. effect([X, T0, T1]) Calculate the heterogeneous treatment effect $$\tau(X, T0, T1)$$. effect_inference([X, T0, T1]) Inference results for the quantities $$\tau(X, T0, T1)$$ produced by the model. effect_interval([X, T0, T1, alpha]) Confidence intervals for the quantities $$\tau(X, T0, T1)$$ produced by the model. fit(Y, T, *[, X, W, sample_weight, ...]) Estimate the counterfactual model from data, i.e. estimates functions τ(·,·,·), ∂τ(·,·). The inference of intercept in the linear model of the constant marginal treatment effect. intercept__interval(*[, alpha]) The intercept in the linear model of the constant marginal treatment effect. marginal_ate(T[, X]) Calculate the average marginal effect $$E_{T, X}[\partial\tau(T, X)]$$. marginal_ate_inference(T[, X]) Inference results for the quantities $$E_{T,X}[\partial \tau(T, X)]$$ produced by the model. marginal_ate_interval(T[, X, alpha]) Confidence intervals for the quantities $$E_{T,X}[\partial \tau(T, X)]$$ produced by the model. marginal_effect(T[, X]) Calculate the heterogeneous marginal effect $$\partial\tau(T, X)$$. Inference results for the quantities $$\partial \tau(T, X)$$ produced by the model. marginal_effect_interval(T[, X, alpha]) Confidence intervals for the quantities $$\partial \tau(T, X)$$ produced by the model. refit_final(*[, inference]) Estimate the counterfactual model using a new final model specification but with cached first stage results. score(Y, T[, X, W, sample_weight]) Score the fitted CATE model on a new data set. shap_values(X, *[, feature_names, ...]) Shap value for the final stage models (const_marginal_effect) summary([alpha, value, decimals, ...]) The summary of coefficient and intercept in the linear model of the constant marginal treatment effect.

Attributes

 bias_part_of_coef coef_ The coefficients in the linear model of the constant marginal treatment effect. dowhy Get an instance of DoWhyWrapper to allow other functionalities from dowhy package. featurizer featurizer_ fit_cate_intercept_ intercept_ The intercept in the linear model of the constant marginal treatment effect. model_cate Get the fitted final CATE model. model_final_ models_nuisance_ models_t Get the fitted models for E[T | X, W]. models_y Get the fitted models for E[Y | X, W]. nuisance_scores_t nuisance_scores_y original_featurizer ortho_learner_model_final_ residuals_ A tuple (y_res, T_res, X, W), of the residuals from the first stage estimation along with the associated X and W. rlearner_model_final_ transformer
ate(X=None, *, T0=0, T1=1)

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 2-dimensional array, the result will be a scalar

Return type

float or (d_y,) array

ate_inference(X=None, *, T0=0, T1=1)

Inference results for the quantity $$E_X[\tau(X, T0, T1)]$$ produced by the model. Available only when inference is not None, 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

object

ate_interval(X=None, *, T0=0, T1=1, alpha=0.05)

Confidence intervals for the quantity $$E_X[\tau(X, T0, T1)]$$ produced by the model. Available only when inference is not None, 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, 1-alpha/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 of ate(X, T0, T1)) )

cate_feature_names(feature_names=None)

Get the output feature names.

Parameters

feature_names (list of str of length X.shape 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 – The names of the output features $$\phi(X)$$, i.e. the features with respect to which the final constant marginal CATE model is linear. It is the names of the features that are associated with each entry of the coef_() parameter. Not available when the featurizer is not None and does not have a method: get_feature_names(feature_names). Otherwise None is returned.

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 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)

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, 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

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

object

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, 1-alpha/2 confidence interval is reported.

Returns

lb, ub – The lower and upper bounds of the confidence interval for each quantity.

Return type

tuple(type of coef_(), type of coef_())

const_marginal_ate(X=None)

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 featurized-T (or T if treatment_featurizer is None) is a vector rather than a 2-dimensional 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)

Inference results for the quantities $$E_X[\theta(X)]$$ produced by the model. Available only when inference is not None, 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

object

const_marginal_ate_interval(X=None, *, alpha=0.05)

Confidence intervals for the quantities $$E_X[\theta(X)]$$ produced by the model. Available only when inference is not None, 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, 1-alpha/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 of const_marginal_ate(X) )

const_marginal_effect(X=None)

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 featurized-T (or T if treatment_featurizer is None) is a vector rather than a 2-dimensional 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)

Inference results for the quantities $$\theta(X)$$ produced by the model. Available only when inference is not None, 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

object

const_marginal_effect_interval(X=None, *, alpha=0.05)

Confidence intervals for the quantities $$\theta(X)$$ produced by the model. Available only when inference is not None, 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, 1-alpha/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 of const_marginal_effect(X) )

effect(X=None, *, T0=0, T1=1)

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 2-dimensional 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 not None, 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

object

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 not None, 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, 1-alpha/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 of effect(X, T0, T1)) )

fit(Y, T, *, X=None, W=None, sample_weight=None, freq_weight=None, sample_var=None, groups=None, cache_values=False, inference='auto')[source]

Estimate the counterfactual model from data, i.e. estimates functions τ(·,·,·), ∂τ(·,·).

Parameters
• Y ((n × d_y) matrix or vector of length n) – Outcomes for each sample

• T ((n × dₜ) matrix or vector of length n) – Treatments for each sample

• X ((n × dₓ) matrix, optional) – Features for each sample

• W ((n × d_w) matrix, optional) – Controls for each sample

• sample_weight ((n,) array_like, optional) – Individual weights for each sample. If None, it assumes equal weight.

• freq_weight ((n,) array_like of int, optional) – Weight for the observation. Observation i is treated as the mean outcome of freq_weight[i] independent observations. When sample_var is not None, this should be provided.

• sample_var ({(n,), (n, d_y)} nd array_like, optional) – Variance of the outcome(s) of the original freq_weight[i] observations that were used to compute the mean outcome represented by observation i.

• groups ((n,) vector, optional) – All rows corresponding to the same group will be kept together during splitting. If groups is not None, the cv argument passed to this class’s initializer must support a ‘groups’ argument to its split method.

• cache_values (bool, default False) – Whether to cache inputs and first stage results, which will allow refitting a different final model

• inference (str, Inference instance, or None) – Method for performing inference. This estimator supports ‘bootstrap’ (or an instance of BootstrapInference) and ‘auto’ (or an instance of LinearModelFinalInference)

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

object

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, 1-alpha/2 confidence interval is reported.

Returns

lower, upper – The lower and upper bounds of the confidence interval.

Return type

tuple(type of intercept_(), type of intercept_())

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 2-dimensional 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 not None, 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

object

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 not None, 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, 1-alpha/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 of marginal_ate(T, X) )

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 $$\{T_i, X_i\}$$. 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 2-dimensional 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 not None, 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

object

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 not None, 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, 1-alpha/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 of marginal_effect(T, X) )

refit_final(*, inference='auto')[source]

Estimate the counterfactual model using a new final model specification but with cached first stage results.

In order for this to succeed, fit must have been called with cache_values=True. This call will only refit the final model. This call we use the current setting of any parameters that change the final stage estimation. If any parameters that change how the first stage nuisance estimates has also been changed then it will have no effect. You need to call fit again to change the first stage estimation results.

Parameters

inference (inference method, optional) – The string or object that represents the inference method

Returns

self – This instance

Return type

object

score(Y, T, X=None, W=None, sample_weight=None)

Score the fitted CATE model on a new data set. Generates nuisance parameters for the new data set based on the fitted residual nuisance models created at fit time. It uses the mean prediction of the models fitted by the different crossfit folds. Then calculates the MSE of the final residual Y on residual T regression.

If model_final does not have a score method, then it raises an AttributeError

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

• sample_weight ((n,) vector, optional) – Weights for each samples

Returns

score – The MSE of the final CATE model on the new data.

Return type

float

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, 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, 1-alpha/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

property model_cate

Get the fitted final CATE model.

Returns

model_cate – An instance of the model_final object that was fitted after calling fit which corresponds to the constant marginal CATE model.

Return type

object of type(model_final)

property models_t

Get the fitted models for E[T | X, W].

Returns

models_t – A nested list of instances of the model_y object. Number of sublist equals to number of monte carlo iterations, each element in the sublist corresponds to a crossfitting fold and is the model instance that was fitted for that training fold.

Return type

nested list of objects of type(model_t)

property models_y

Get the fitted models for E[Y | X, W].

Returns

models_y – A nested list of instances of the model_y object. Number of sublist equals to number of monte carlo iterations, each element in the sublist corresponds to a crossfitting fold and is the model instance that was fitted for that training fold.

Return type

nested list of objects of type(model_y)

property residuals_

A tuple (y_res, T_res, X, W), of the residuals from the first stage estimation along with the associated X and W. Samples are not guaranteed to be in the same order as the input order.