# econml.dr.SparseLinearDRLearner

class econml.dr.SparseLinearDRLearner(*, model_propensity='auto', model_regression='auto', featurizer=None, fit_cate_intercept=True, alpha='auto', n_alphas=100, alpha_cov='auto', n_alphas_cov=10, max_iter=1000, tol=0.0001, n_jobs=None, min_propensity=1e-06, categories='auto', cv=2, mc_iters=None, mc_agg='mean', random_state=None)[source]

Special case of the DRLearner where the final stage is a Debiased Lasso Regression. In this case, inference can be performed via the debiased lasso approach and its asymptotic normal characterization of the estimated parameters. This is computationally faster than bootstrap inference. Leave the default inference='auto' unchanged, or explicitly set inference='debiasedlasso' at fit time to enable inference via asymptotic normality.

More concretely, this estimator assumes that the final cate model for each treatment takes a linear form:

$\theta_t(X) = \left\langle \theta_t, \phi(X) \right\rangle + \beta_t$

where $$\phi(X)$$ is the outcome features of the featurizers, or X if featurizer is None. $$\beta_t$$ is a an intercept of the CATE, which is included if fit_cate_intercept=True (Default). It fits this by running a debiased lasso regression (i.e. $$\ell_1$$-penalized regression with debiasing), regressing the doubly robust outcome differences on X: i.e. first solves the penalized square loss problem

$\min_{\theta_t, \beta_t} E_n\left[\left(Y_{i, t}^{DR} - Y_{i, 0}^{DR} - \left\langle \theta_t, \phi(X_i) \right\rangle - \beta_t\right)^2\right] + \lambda \left\lVert \theta_t \right\rVert_1$

and then adds a debiasing correction to the solution. If alpha=’auto’ (recommended), then the penalty weight $$\lambda$$ is set optimally via cross-validation.

This approach is valid even if the CATE model is not linear in $$\phi(X)$$. In this case it performs inference on the best sparse linear approximation of the CATE model.

Parameters
• model_propensity (scikit-learn classifier or ‘auto’, optional (default=’auto’)) – Estimator for Pr[T=t | X, W]. Trained by regressing treatments on (features, controls) concatenated. 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. If ‘auto’, LogisticRegressionCV will be chosen.

• model_regression (scikit-learn regressor or ‘auto’, optional (default=’auto’)) – Estimator for E[Y | X, W, T]. Trained by regressing Y on (features, controls, one-hot-encoded treatments) concatenated. The one-hot-encoding excludes the baseline treatment. Must implement fit and predict methods. If different models per treatment arm are desired, see the MultiModelWrapper helper class. If ‘auto’ WeightedLassoCV/WeightedMultiTaskLassoCV will be chosen.

• featurizer (transformer, optional, default None) – 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, optional, default True) – Whether the linear CATE model should have a constant term.

• alpha (string | float, optional., default ‘auto’.) – CATE L1 regularization applied through the debiased lasso in the final model. ‘auto’ corresponds to a CV form of the DebiasedLasso.

• n_alphas (int, optional, default 100) – How many alphas to try if alpha=’auto’

• alpha_cov (string | float, optional, default ‘auto’) – The regularization alpha that is used when constructing the pseudo inverse of the covariance matrix Theta used to for correcting the final state lasso coefficient in the debiased lasso. Each such regression corresponds to the regression of one feature on the remainder of the features.

• n_alphas_cov (int, optional, default 10) – How many alpha_cov to try if alpha_cov=’auto’.

• max_iter (int, optional, default 1000) – The maximum number of iterations in the Debiased Lasso

• tol (float, optional, default 1e-4) – The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.

• n_jobs (int or None, optional (default=None)) – The number of jobs to run in parallel for both fit and predict. None means 1 unless in a joblib.parallel_backend() context. -1 means using all processors.

• min_propensity (float, optional, default 1e-6) – The minimum propensity at which to clip propensity estimates to avoid dividing by zero.

• 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, optional, 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(X,T) to generate the splits.

• mc_iters (int, optional (default=None)) – The number of times to rerun the first stage models to reduce the variance of the nuisances.

• mc_agg ({‘mean’, ‘median’}, optional (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) – 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.

Examples

A simple example with the default models:

from econml.dr import DRLearner, SparseLinearDRLearner

np.random.seed(123)
X = np.random.normal(size=(1000, 3))
T = np.random.binomial(2, scipy.special.expit(X[:, 0]))
y = (1 + .5*X[:, 0]) * T + X[:, 0] + np.random.normal(size=(1000,))
est = SparseLinearDRLearner()
est.fit(y, T, X=X, W=None)

>>> est.effect(X[:3])
array([ 0.41...,  0.31..., -0.12...])
>>> est.effect_interval(X[:3])
(array([-0.02..., -0.29... , -0.84...]), array([0.84..., 0.92..., 0.59...]))
>>> est.coef_(T=1)
array([ 0.45..., -0.00..., 0.06...])
>>> est.coef__interval(T=1)
(array([ 0.20..., -0.23..., -0.17...]), array([0.69..., 0.23..., 0.30...]))
>>> est.intercept_(T=1)
0.88...
>>> est.intercept__interval(T=1)
(0.64..., 1.11...)

score_

The MSE in the final doubly robust potential outcome regressions, i.e.

$\frac{1}{n_t} \sum_{t=1}^{n_t} \frac{1}{n} \sum_{i=1}^n (Y_{i, t}^{DR} - \hat{\theta}_t(X_i))^2$

where n_t is the number of treatments (excluding control).

If sample_weight is not None at fit time, then a weighted average across samples is returned.

Type

float

__init__(*, model_propensity='auto', model_regression='auto', featurizer=None, fit_cate_intercept=True, alpha='auto', n_alphas=100, alpha_cov='auto', n_alphas_cov=10, max_iter=1000, tol=0.0001, n_jobs=None, min_propensity=1e-06, categories='auto', cv=2, mc_iters=None, mc_agg='mean', random_state=None)[source]

Methods

 __init__(*[, model_propensity, ...]) 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 coefficients in the linear model of the constant marginal treatment effect associated with treatment T. The inference for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T. coef__interval(T, *[, alpha]) The confidence interval for the coefficients in the linear model of the constant marginal treatment effect associated with treatment T. 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, groups, ...]) Estimate the counterfactual model from data, i.e. estimates function $$\theta(\cdot)$$. The intercept in the linear model of the constant marginal treatment effect associated with treatment T. The inference of the intercept in the linear model of the constant marginal treatment effect associated with treatment T. intercept__interval(T, *[, alpha]) The intercept in the linear model of the constant marginal treatment effect associated with treatment T. 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. model_cate([T]) Get the fitted final CATE 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(T, *[, alpha, value, decimals, ...]) The summary of coefficient and intercept in the linear model of the constant marginal treatment effect associated with treatment T.

Attributes

 dowhy Get an instance of DoWhyWrapper to allow other functionalities from dowhy package. featurizer_ Get the fitted featurizer. fit_cate_intercept_ fitted_models_final model_final model_final_ models_nuisance_ models_propensity Get the fitted propensity models. models_regression Get the fitted regression models. multitask_model_cate Get the fitted final CATE model. multitask_model_final nuisance_scores_propensity Gets the score for the propensity model on out-of-sample training data nuisance_scores_regression Gets the score for the regression model on out-of-sample training data ortho_learner_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 (optional (m, d_x) matrix) – 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 (optional (m, d_x) matrix) – Features for each sample

• T0 (optional (m, d_t) matrix or vector of length m (Default=0)) – Base treatments for each sample

• T1 (optional (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 (optional (m, d_x) matrix) – Features for each sample

• T0 (optional (m, d_t) matrix or vector of length m (Default=0)) – Base treatments for each sample

• T1 (optional (m, d_t) matrix or vector of length m (Default=1)) – Target treatments for each sample

• alpha (optional 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 strings 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 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 strings 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 strings 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 strings

cate_treatment_names(treatment_names=None)

Get treatment names.

If the treatment is discrete, it will return expanded treatment names.

Parameters

treatment_names (list of strings of length T.shape 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

out_treatment_names – Returns (possibly expanded) treatment names.

Return type

list of strings

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

object

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 (optional 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 for each quantity.

Return type

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

const_marginal_ate(X=None)

Calculate the average constant marginal CATE $$E_X[\theta(X)]$$.

Parameters

X (optional (m, d_x) matrix or None (Default=None)) – Features for each sample.

Returns

theta – Average constant marginal CATE of each treatment 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) matrix

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 (optional (m, d_x) matrix or None (Default=None)) – 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 (optional (m, d_x) matrix or None (Default=None)) – Features for each sample

• alpha (optional 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 (optional (m, d_x) matrix or None (Default=None)) – Features for each sample.

Returns

theta – Constant marginal CATE of each treatment on each outcome for each sample X[i]. 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) matrix or (d_y, d_t) matrix if X is None

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 (optional (m, d_x) matrix or None (Default=None)) – 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 (optional (m, d_x) matrix or None (Default=None)) – Features for each sample

• alpha (optional 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 (optional (m, d_x) matrix) – 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 (optional (m, d_x) matrix) – Features for each sample

• T0 (optional (m, d_t) matrix or vector of length m (Default=0)) – Base treatments for each sample

• T1 (optional (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 (optional (m, d_x) matrix) – Features for each sample

• T0 (optional (m, d_t) matrix or vector of length m (Default=0)) – Base treatments for each sample

• T1 (optional (m, d_t) matrix or vector of length m (Default=1)) – Target treatments for each sample

• alpha (optional 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, groups=None, cache_values=False, inference='auto')[source]

Estimate the counterfactual model from data, i.e. estimates function $$\theta(\cdot)$$.

Parameters
• Y ((n,) vector of length n) – Outcomes for each sample

• T ((n,) vector of length n) – Treatments for each sample

• X (optional(n, d_x) matrix or None (Default=None)) – Features for each sample

• W (optional(n, d_w) matrix or None (Default=None)) – Controls for each sample

• sample_weight ((n,) array like or None) – Individual weights for each sample. If None, it assumes equal weight.

• 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 (string, Inference instance, or None) – Method for performing inference. This estimator supports 'bootstrap' (or an instance of BootstrapInference) and 'debiasedlasso' (or an instance of LinearModelInferenceDiscrete).

Returns

self

Return type

DRLearner instance

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

object

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 (optional 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_(T), type of intercept_(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 (optional (m, d_x) matrix) – 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 (optional (m, d_x) matrix or None (Default=None)) – 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 (optional (m, d_x) matrix or None (Default=None)) – Features for each sample

• alpha (optional 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 $$\{T_i, X_i\}$$. Since this class assumes a linear model, the base treatment is ignored in this calculation.

Parameters
• T ((m, d_t) matrix) – Base treatments for each sample

• X (optional (m, d_x) matrix) – 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 (optional (m, d_x) matrix or None (Default=None)) – 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 (optional (m, d_x) matrix or None (Default=None)) – Features for each sample

• alpha (optional 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) )

model_cate(T=1)

Get the fitted final CATE model.

Parameters

T (alphanumeric) – The treatment with respect to which we want the fitted CATE model.

Returns

model_cate – An instance of the model_final object that was fitted after calling fit which corresponds to the CATE model for treatment T=t, compared to baseline. Available when multitask_model_final=False.

Return type

object of type(model_final)

refit_final(*, inference='auto')

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,) vector of length n) – Outcomes for each sample

• T ((n,) vector of length n) – Treatments for each sample

• X (optional(n, d_x) matrix or None (Default=None)) – Features for each sample

• W (optional(n, d_w) matrix or None (Default=None)) – Controls for each sample

• sample_weight (optional(n,) vector or None (Default=None)) – 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 (optional None or list of strings of length X.shape (Default=None)) – The names of input features.

• treatment_names (optional None or list (Default=None)) – The name of 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 (optional None or list (Default=None)) – The name of the outcome.

• background_samples (int or None, (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(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 (optional 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 (optinal float (default=0)) – The mean value of the metric you’d like to test under null hypothesis.

• decimals (optinal int (default=3)) – Number of decimal places to round each column to.

• feature_names (optional list of strings or None (default is None)) – The input of the feature names

• treatment_names (optional list of strings or None (default is None)) – The names of the treatments

• output_names (optional list of strings or None (default is None)) – 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

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 models_propensity

Get the fitted propensity models.

Returns

models_propensity – A nested list of instances of the model_propensity 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_propensity)

property models_regression

Get the fitted regression models.

Returns

model_regression – A nested list of instances of the model_regression 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_regression)

Get the fitted final CATE model.

Returns

multitask_model_cate – An instance of the model_final object that was fitted after calling fit which corresponds whose vector of outcomes correspond to the CATE model for each treatment, compared to baseline. Available only when multitask_model_final=True.

Return type

object of type(model_final)

property nuisance_scores_propensity

Gets the score for the propensity model on out-of-sample training data

property nuisance_scores_regression

Gets the score for the regression model on out-of-sample training data