# econml.dr.DRLearner

class econml.dr.DRLearner(*, model_propensity='auto', model_regression='auto', model_final=StatsModelsLinearRegression(), multitask_model_final=False, featurizer=None, min_propensity=1e-06, categories='auto', cv=2, mc_iters=None, mc_agg='mean', random_state=None)[source]

CATE estimator that uses doubly-robust correction techniques to account for covariate shift (selection bias) between the treatment arms. The estimator 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. If we let:

$Y_{i, t}^{DR} = E[Y | X_i, W_i, T_i=t] + \frac{Y_i - E[Y | X_i, W_i, T_i=t]}{Pr[T_i=t | X_i, W_i]} \cdot 1\{T_i=t\}$

Then the following estimating equation holds:

$E\left[Y_{i, t}^{DR} - Y_{i, 0}^{DR} | X_i\right] = \theta_t(X_i)$

Thus if we estimate the nuisance functions $$h(X, W, T) = E[Y | X, W, T]$$ and $$p_t(X, W)=Pr[T=t | X, W]$$ in the first stage, we can estimate the final stage cate for each treatment t, by running a regression, regressing $$Y_{i, t}^{DR} - Y_{i, 0}^{DR}$$ on $$X_i$$.

The problem of estimating the nuisance function $$p$$ is a simple multi-class classification problem of predicting the label $$T$$ from $$X, W$$. The DRLearner class takes as input the parameter model_propensity, which is an arbitrary scikit-learn classifier, that is internally used to solve this classification problem.

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

The final stage is multi-task regression problem with outcomes the labels $$Y_{i, t}^{DR} - Y_{i, 0}^{DR}$$ for each non-baseline treatment t. The DRLearner takes as input parameter model_final, which is any scikit-learn regressor that is internally used to solve this multi-task regresion problem. If the parameter multitask_model_final is False, then this model is assumed to be a mono-task regressor, and separate clones of it are used to solve each regression target separately.

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.

• model_final – estimator for the final cate model. Trained on regressing the doubly robust potential outcomes on (features X).

• If X is None, then the fit method of model_final should be able to handle X=None.

• If featurizer is not None and X is not None, then it is trained on the outcome of featurizer.fit_transform(X).

• If multitask_model_final is True, then this model must support multitasking and it is trained by regressing all doubly robust target outcomes on (featurized) features simultanteously.

• The output of the predict(X) of the trained model will contain the CATEs for each treatment compared to baseline treatment (lexicographically smallest). If multitask_model_final is False, it is assumed to be a mono-task model and a separate clone of the model is trained for each outcome. Then predict(X) of the t-th clone will be the CATE of the t-th lexicographically ordered treatment compared to the baseline.

• multitask_model_final (bool, optional, default False) – Whether the model_final should be treated as a multi-task model. See description of model_final.

• 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.

• 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 is 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 (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

np.random.seed(123)
X = np.random.normal(size=(1000, 3))
T = np.random.binomial(2, scipy.special.expit(X[:, 0]))
sigma = 0.001
y = (1 + .5*X[:, 0]) * T + X[:, 0] + np.random.normal(0, sigma, size=(1000,))
est = DRLearner()
est.fit(y, T, X=X, W=None)

>>> est.const_marginal_effect(X[:2])
array([[0.511640..., 1.144004...],
[0.378140..., 0.613143...]])
>>> est.effect(X[:2], T0=0, T1=1)
array([0.511640..., 0.378140...])
>>> est.score_
5.11238581...
>>> est.score(y, T, X=X)
5.78673506...
>>> est.model_cate(T=1).coef_
array([0.434910..., 0.010226..., 0.047913...])
>>> est.model_cate(T=2).coef_
array([ 0.863723...,  0.086946..., -0.022288...])
>>> est.cate_feature_names()
['X0', 'X1', 'X2']
>>> [mdl.coef_ for mdls in est.models_regression for mdl in mdls]
[array([ 1.472...,  0.001..., -0.011...,  0.698..., 2.049...]),
array([ 1.455..., -0.002...,  0.005...,  0.677...,  1.998...])]
>>> [mdl.coef_ for mdls in est.models_propensity for mdl in mdls]
[array([[-0.747...,  0.153..., -0.018...],
[ 0.083..., -0.110..., -0.076...],
[ 0.663..., -0.043... ,  0.094...]]),
array([[-1.048...,  0.000...,  0.032...],
[ 0.019...,  0.124..., -0.081...],
[ 1.029..., -0.124...,  0.049...]])]


Beyond default models:

from sklearn.linear_model import LassoCV
from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor
from econml.dr import DRLearner

np.random.seed(123)
X = np.random.normal(size=(1000, 3))
T = np.random.binomial(2, scipy.special.expit(X[:, 0]))
sigma = 0.01
y = (1 + .5*X[:, 0]) * T + X[:, 0] + np.random.normal(0, sigma, size=(1000,))
est = DRLearner(model_propensity=RandomForestClassifier(n_estimators=100, min_samples_leaf=10),
model_regression=RandomForestRegressor(n_estimators=100, min_samples_leaf=10),
model_final=LassoCV(cv=3),
featurizer=None)
est.fit(y, T, X=X, W=None)

>>> est.score_
1.7...
>>> est.const_marginal_effect(X[:3])
array([[0.68...,  1.10...],
[0.56...,  0.79...],
[0.34...,  0.10...]])
>>> est.model_cate(T=2).coef_
array([0.74..., 0.        , 0.        ])
>>> est.model_cate(T=2).intercept_
1.9...
>>> est.model_cate(T=1).coef_
array([0.24..., 0.00..., 0.        ])
>>> est.model_cate(T=1).intercept_
0.94...

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', model_final=StatsModelsLinearRegression(), multitask_model_final=False, featurizer=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. 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 function $$\theta(\cdot)$$. 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)

Attributes

 dowhy Get an instance of DoWhyWrapper to allow other functionalities from dowhy package. featurizer_ Get the fitted featurizer. fitted_models_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. 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)[source]

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

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, 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,) 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, default None) – Individual weights for each sample. If None, it assumes equal weight.

• freq_weight ((n,) array like of integers, default None) – 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,) nd array like, default None) – 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 (string, Inference instance, or None) – Method for performing inference. This estimator supports ‘bootstrap’ (or an instance of BootstrapInference).

Returns

self

Return type

DRLearner instance

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)[source]

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')[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)[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,) 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)[source]

Shap value for the final stage models (const_marginal_effect)

Parameters
• X ((m, d_x) matrix) – Features for each sample. Should be in the same shape of fitted X in final stage.

• feature_names (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

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