econml.iv.dml.NonParamDMLIV

class econml.iv.dml.NonParamDMLIV(*, model_Y_X, model_T_X, model_T_XZ, model_final, featurizer=None, cv=2, mc_iters=None, mc_agg='mean', discrete_instrument=False, discrete_treatment=False, categories='auto', random_state=None)[source]

Bases: econml.iv.dml._dml._BaseDMLIV

A child of the _BaseDMLIV class that allows for an arbitrary square loss based ML method in the final stage of the DMLIV algorithm. The method has to support sample weights and the fit method has to take as input sample_weights (e.g. random forests), i.e. fit(X, y, sample_weight=None) It achieves this by re-writing the final stage square loss of the DMLIV algorithm as:

\[\sum_i (\E[T|X_i, Z_i] - \E[T|X_i])^2 * ((Y_i - \E[Y|X_i])/(\E[T|X_i, Z_i] - \E[T|X_i]) - \theta(X))^2\]

Then this can be viewed as a weighted square loss regression, where the target label is

\[\tilde{Y}_i = (Y_i - \E[Y|X_i])/(\E[T|X_i, Z_i] - \E[T|X_i])\]

and each sample has a weight of

\[V(X_i) = (\E[T|X_i, Z_i] - \E[T|X_i])^2\]

Thus we can call any regression model with inputs:

fit(X, \(\tilde{Y}_i\), sample_weight= \(V(X_i)\))

Parameters
  • model_Y_X (estimator) – model to estimate \(\E[Y | X]\). Must support fit and predict methods.

  • model_T_X (estimator) – model to estimate \(\E[T | X]\). Must support fit and either predict or predict_proba methods, depending on whether the treatment is discrete.

  • model_T_XZ (estimator) – model to estimate \(\E[T | X, Z]\). Must support fit and either predict or predict_proba methods, depending on whether the treatment is discrete.

  • model_final (estimator) – final model for predicting \(\tilde{Y}\) from X with sample weights V(X)

  • 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(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 (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.

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

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

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

  • random_state (int, RandomState instance or None, optional (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.

__init__(*, model_Y_X, model_T_X, model_T_XZ, model_final, featurizer=None, cv=2, mc_iters=None, mc_agg='mean', discrete_instrument=False, discrete_treatment=False, categories='auto', random_state=None)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(*, model_Y_X, model_T_X, …[, …])

Initialize self.

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.

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 CATE \(\theta(·)\).

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, Z[, X, sample_weight, …])

Estimate the counterfactual model from data, i.e.

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.

refit_final([inference])

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

score(Y, T, Z[, X])

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_

model_cate

Get the fitted final CATE model.

model_final_

models_T_X

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

models_T_XZ

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

models_Y_X

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

models_nuisance_

nuisance_scores_T_X

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

nuisance_scores_T_XZ

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

nuisance_scores_Y_X

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

original_featurizer

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=0.1)

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=0.1)) – 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[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 constant marginal CATE model is linear. It is the names of the features that are associated with each entry of the coef_() parameter. Not available when the featurizer is not None and does not have a method: get_feature_names(feature_names). Otherwise None is returned.

Return type

list of 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[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 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[1] 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=0.1)

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=0.1)) – 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=0.1)

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=0.1)) – 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=0.1)

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=0.1)) – 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, *, sample_weight=None, freq_weight=None, sample_var=None, groups=None, cache_values=False, inference=None)

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 (optional(n, d_x) matrix or None (Default=None)) – Features 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,), (n, d_y)} 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,:class:.Inference instance, or None) – Method for performing inference. This estimator supports ‘bootstrap’ (or an instance of:class:.BootstrapInference).

Returns

self

Return type

_BaseDMLIV

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=0.1)

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=0.1)) – 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=0.1)

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=0.1)) – 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=None)

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)

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 (optional(n, d_z) matrix) – Instruments for each sample

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

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[1] (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 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_X

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

Returns

models_T_X – A nested list of instances of the model_T_X 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_X)

property models_T_XZ

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

Returns

models_T_XZ – A nested list of instances of the model_T_XZ 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_XZ)

property models_Y_X

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

Returns

models_Y_X – A nested list of instances of the model_Y_X 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_X)

property nuisance_scores_T_X

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

property nuisance_scores_T_XZ

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

property nuisance_scores_Y_X

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