econml.iv.dml.OrthoIV

class econml.iv.dml.OrthoIV(*, model_y_xw='auto', model_t_xw='auto', model_t_xwz='auto', model_z_xw='auto', projection=False, featurizer=None, fit_cate_intercept=True, discrete_outcome=False, discrete_treatment=False, treatment_featurizer=None, discrete_instrument=False, categories='auto', cv=2, mc_iters=None, mc_agg='mean', random_state=None, allow_missing=False)[source]

Implementation of the orthogonal/double ml method for CATE estimation with IV as described in section 4.2:

Double/Debiased Machine Learning for Treatment and Causal Parameters Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, James Robins https://arxiv.org/abs/1608.00060

Solve the following moment equation:

$\E[(Y-\E[Y|X]-\theta(X) * (T-\E[T|X]))(Z-\E[Z|X])] = 0$
Parameters
• model_y_xw (estimator, default 'auto') – Determines how to fit the outcome to the features and controls ($$\E[Y | X, W]$$).

• If 'auto', the model will be the best-fitting of a set of linear and forest models

• Otherwise, see Model Selection for the range of supported options; if a single model is specified it should be a classifier if discrete_outcome is True and a regressor otherwise

• model_t_xw (estimator, default 'auto') – Determines how to fit the treatment to the features and controls ($$\E[T | X, W]$$).

• If 'auto', the model will be the best-fitting of a set of linear and forest models

• Otherwise, see Model Selection for the range of supported options; if a single model is specified it should be a classifier if discrete_treatment is True and a regressor otherwise

• model_t_xwz (estimator, default 'auto') – Determines how to fit the treatment to the features, controls, and instrument ($$\E[T | X, W, Z]$$).

• If 'auto', the model will be the best-fitting of a set of linear and forest models

• Otherwise, see Model Selection for the range of supported options; if a single model is specified it should be a classifier if discrete_treatment is True and a regressor otherwise

• model_z_xw (estimator, default 'auto') – Determines how to fit the instrument to the features and controls ($$\E[Z | X, W]$$).

• If 'auto', the model will be the best-fitting of a set of linear and forest models

• Otherwise, see Model Selection for the range of supported options; if a single model is specified it should be a classifier if discrete_instrument is True and a regressor otherwise

• projection (bool, default False) – If True, we fit a slight variant of OrthoIV where we use E[T|X, W, Z] as the instrument as opposed to Z, model_z_xw will be disabled; If False, model_t_xwz will be disabled.

• 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.

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

• discrete_outcome (bool, default False) – Whether the outcome should be treated as binary

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

• 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.

• discrete_instrument (bool, default False) – Whether the instrument 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.

• 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[0], 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 W. If True, will need to supply nuisance models that can handle missing values.

Examples

A simple example with the default models:

from econml.iv.dml import OrthoIV

# Define the data generation functions
def dgp(n, p, true_fn):
X = np.random.normal(0, 1, size=(n, p))
Z = np.random.binomial(1, 0.5, size=(n,))
nu = np.random.uniform(0, 10, size=(n,))
coef_Z = 0.8
C = np.random.binomial(
1, coef_Z * scipy.special.expit(0.4 * X[:, 0] + nu)
)  # Compliers when recomended
C0 = np.random.binomial(
1, 0.06 * np.ones(X.shape[0])
)  # Non-compliers when not recommended
T = C * Z + C0 * (1 - Z)
y = true_fn(X) * T + 2 * nu + 5 * (X[:, 3] > 0) + 0.1 * np.random.uniform(0, 1, size=(n,))
return y, T, Z, X

def true_heterogeneity_function(X):
return 5 * X[:, 0]

np.random.seed(123)
y, T, Z, X = dgp(1000, 5, true_heterogeneity_function)
est = OrthoIV(discrete_treatment=True, discrete_instrument=True)
est.fit(Y=y, T=T, Z=Z, X=X)

>>> est.effect(X[:3])
array([-4.28045... ,  6.02945..., -2.86851...])
>>> est.effect_interval(X[:3])
(array([-7.20729...,  1.75412..., -5.20897...]),
array([-1.35361..., 10.30478..., -0.52805...]))
>>> est.coef_
array([ 4.51659...,  0.78512...,  0.23706...,  0.24126... , -0.47167...])
>>> est.coef__interval()
(array([ 3.15602..., -0.35785..., -0.89798..., -0.90530..., -1.62445...]),
array([5.87715... , 1.92810... , 1.37211..., 1.38783..., 0.68110...]))
>>> est.intercept_
-0.13672...
>>> est.intercept__interval()
(-1.27036..., 0.99690...)

__init__(*, model_y_xw='auto', model_t_xw='auto', model_t_xwz='auto', model_z_xw='auto', projection=False, featurizer=None, fit_cate_intercept=True, discrete_outcome=False, discrete_treatment=False, treatment_featurizer=None, discrete_instrument=False, categories='auto', cv=2, mc_iters=None, mc_agg='mean', random_state=None, allow_missing=False)[source]

Methods

 __init__(*[, model_y_xw, model_t_xw, ...]) 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, *, Z[, X, W, sample_weight, ...]) Estimate the counterfactual model from data, i.e. estimates function $$\theta(\cdot)$$. 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, Z[, 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_ Get the fitted 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 model_final_ models_nuisance_ models_t_xw Get the fitted models for $$\E[T | X]$$. models_t_xwz Get the fitted models for $$\E[T | X, Z]$$. models_y_xw Get the fitted models for $$\E[Y | X]$$. models_z_xw Get the fitted models for $$\E[Z | X]$$. nuisance_scores_t_xw Get the scores for t_xw model on the out-of-sample training data nuisance_scores_t_xwz Get the scores for t_xwz model on the out-of-sample training data nuisance_scores_y_xw Get the scores for y_xw model on the out-of-sample training data nuisance_scores_z_xw Get the scores for z_xw model on the out-of-sample training data original_featurizer ortho_learner_model_final_ residuals_ A tuple (y_res, T_res,Z_res, X, W, Z), of the residuals from the first stage estimation along with the associated X, W and Z. 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)[source]

Get the output feature names.

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 – The names of the output features $$\phi(X)$$, i.e. the features with respect to which the final CATE model for each treatment is linear. It is the names of the features that are associated with each entry of the coef_() parameter. Available only when the featurizer is not None and has 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[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)

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

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, *, Z, 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 function $$\theta(\cdot)$$.

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

• Z ((n, d_z) matrix) – Instruments 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,) 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:class:.BootstrapInference) and ‘auto’ (or an instance of LinearModelFinalInference)

Returns

self

Return type

OrthoIV instance

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, Z, X=None, W=None, sample_weight=None)[source]

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

• Z ((n, d_z) matrix, optional) – Instruments 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[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, 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 featurizer_

Get the fitted featurizer.

Returns

featurizer – An instance of the fitted featurizer that was used to preprocess X in the final CATE model training. Available only when featurizer is not None and X is not None.

Return type

object of type(featurizer)

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_xw

Get the fitted models for $$\E[T | X]$$.

Returns

models_t_xw – A nested list of instances of the model_t_xw 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_xw)

property models_t_xwz

Get the fitted models for $$\E[T | X, Z]$$.

Returns

models_t_xwz – A nested list of instances of the model_t_xwz 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_xwz)

property models_y_xw

Get the fitted models for $$\E[Y | X]$$.

Returns

models_y_xw – A nested list of instances of the model_y_xw 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_xw)

property models_z_xw

Get the fitted models for $$\E[Z | X]$$.

Returns

models_z_xw – A nested list of instances of the model_z_xw 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_z_xw)

property nuisance_scores_t_xw

Get the scores for t_xw model on the out-of-sample training data

property nuisance_scores_t_xwz

Get the scores for t_xwz model on the out-of-sample training data

property nuisance_scores_y_xw

Get the scores for y_xw model on the out-of-sample training data

property nuisance_scores_z_xw

Get the scores for z_xw model on the out-of-sample training data

property residuals_

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