econml.metalearners.XLearner

class econml.metalearners.XLearner(*, models, cate_models=None, propensity_model=LogisticRegression(), categories='auto', allow_missing=False)[source]

Bases: econml._cate_estimator.TreatmentExpansionMixin, econml._cate_estimator.LinearCateEstimator

Meta-algorithm proposed by Kunzel et al. that performs best in settings: where the number of units in one treatment arm is much larger than others.

Parameters

models (outcome estimators for both control units and treatment units) – It can be a single estimator applied to all the control and treatment units or a tuple/list of estimators with one estimator per treatment (including control). Must implement fit and predict methods.
cate_models (estimator for pseudo-treatment effects on control and treatments) – It can be a single estimator applied to all the control and treatments or a tuple/list of estimators with one estimator per treatment (including control). If None, it will be same models as the outcome estimators. Must implement fit and predict methods.
propensity_model (estimator for the propensity function) – Must implement fit and predict_proba methods. The fit method must be able to accept X and T, where T is a shape (n, ) array.
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.
allow_missing (bool) – Whether to allow missing values in X. If True, will need to supply models, cate_models, and propensity_model that can handle missing values.

Examples

A simple example:

from econml.metalearners import XLearner
from sklearn.linear_model import LinearRegression

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 = XLearner(models=LinearRegression())
est.fit(y, T, X=X)

>>> est.effect(X[:3])
array([0.58547..., 1.82860..., 0.78379...])

__init__(*, models, cate_models=None, propensity_model=LogisticRegression(), categories='auto', allow_missing=False)[source]

Methods

`__init__`(*, models[, cate_models, ...])
`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])	Public interface for getting feature names.
`cate_output_names`([output_names])	Public interface for getting output names.
`cate_treatment_names`([treatment_names])	Get treatment names.
`const_marginal_ate`([X])	Calculate the average constant marginal CATE \(E_X[\theta(X)]\).
`const_marginal_ate_inference`([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.
`const_marginal_effect`(X)	Calculate the constant marginal treatment effect on a vector of features for each sample.
`const_marginal_effect_inference`([X])	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[, inference])	Build an instance of XLearner.
`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 \(\partial\tau(T, X)\).
`marginal_effect_inference`(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.
`shap_values`(X, *[, feature_names, ...])	Shap value for the final stage models (const_marginal_effect)

Attributes

`dowhy`	Get an instance of `DoWhyWrapper` to allow other functionalities from dowhy package.
`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)

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)

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

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)[source]

Calculate the constant marginal treatment effect on a vector of features for each sample.

Parameters: X (matrix, shape (m × dₓ)) – Matrix of features for each sample.
Returns: τ_hat – Constant marginal CATE of each treatment on each outcome for each sample X[i]. Note that when Y is a vector rather than a 2-dimensional array, the corresponding singleton dimensions in the output will be collapsed
Return type: matrix, shape (m, d_y, 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, inference=None)[source]

Build an instance of XLearner.

Parameters

Y (array_like, shape (n, ) or (n, d_y)) – Outcome(s) for the treatment policy.
T (array_like, shape (n, ) or (n, 1)) – Treatment policy. Only binary treatments are accepted as input. T will be flattened if shape is (n, 1).
X (array_like, shape (n, d_x)) – Feature vector that captures heterogeneity.
inference (str, Inference instance, or None) – Method for performing inference. This estimator supports ‘bootstrap’ (or an instance of BootstrapInference)

Returns

self

Return type

an instance of 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 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) )

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

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