# econml.orf.DROrthoForest¶

class econml.orf.DROrthoForest(*, n_trees=500, min_leaf_size=10, max_depth=10, subsample_ratio=0.7, bootstrap=False, lambda_reg=0.01, propensity_model=LogisticRegression(penalty='l1', solver='saga'), model_Y=<econml.sklearn_extensions.linear_model.WeightedLassoCVWrapper object>, propensity_model_final=None, model_Y_final=None, categories='auto', n_jobs=-1, backend='loky', verbose=3, batch_size='auto', random_state=None)[source]

Bases: econml.orf._ortho_forest.BaseOrthoForest

OrthoForest for discrete treatments using the doubly robust moment function.

A two-forest approach for learning heterogeneous treatment effects using kernel two stage estimation.

Parameters
• n_trees (integer, optional (default=500)) – Number of causal estimators in the forest.

• min_leaf_size (integer, optional (default=10)) – The minimum number of samples in a leaf.

• max_depth (integer, optional (default=10)) – The maximum number of splits to be performed when expanding the tree.

• subsample_ratio (float, optional (default=0.7)) – The ratio of the total sample to be used when training a causal tree. Values greater than 1.0 will be considered equal to 1.0. Parameter is ignored when bootstrap=True.

• bootstrap (boolean, optional (default=False)) – Whether to use bootstrap subsampling.

• lambda_reg (float, optional (default=0.01)) – The regularization coefficient in the ell_2 penalty imposed on the locally linear part of the second stage fit. This is not applied to the local intercept, only to the coefficient of the linear component.

• propensity_model (estimator, optional (default=sklearn.linear_model.LogisticRegression(penalty=’l1’, solver=’saga’, multi_class=’auto’))) – Model for estimating propensity of treatment at each leaf. Will be trained on features and controls (concatenated). Must implement fit and predict_proba methods.

• model_Y (estimator, optional (default=sklearn.linear_model.LassoCV(cv=3))) – Estimator for learning potential outcomes at each leaf. Will be trained on features, controls and one hot encoded treatments (concatenated). If different models per treatment arm are desired, see the MultiModelWrapper helper class. The model(s) must implement fit and predict methods.

• propensity_model_final (estimator, optional (default=None)) – Model for estimating propensity of treatment at at prediction time. Will be trained on features and controls (concatenated). Must implement fit and predict_proba methods. If parameter is set to None, it defaults to the value of propensity_model parameter.

• model_Y_final (estimator, optional (default=None)) – Estimator for learning potential outcomes at prediction time. Will be trained on features, controls and one hot encoded treatments (concatenated). If different models per treatment arm are desired, see the MultiModelWrapper helper class. The model(s) must implement fit and predict methods. If parameter is set to None, it defaults to the value of model_Y parameter.

• categories (‘auto’ or list) – 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.

• n_jobs (int, optional (default=-1)) – The number of jobs to run in parallel for both fit() and effect(). -1 means using all processors. Since OrthoForest methods are computationally heavy, it is recommended to set n_jobs to -1.

• backend (‘threading’ or ‘loky’, optional (default=’loky’)) – What backend should be used for parallelization with the joblib library.

• verbose (int, optional (default=3)) – Verbosity level

• batch_size (int or ‘auto’, optional (default=’auto’)) – Batch_size of jobs for parallelism

• 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__(*, n_trees=500, min_leaf_size=10, max_depth=10, subsample_ratio=0.7, bootstrap=False, lambda_reg=0.01, propensity_model=LogisticRegression(penalty='l1', solver='saga'), model_Y=<econml.sklearn_extensions.linear_model.WeightedLassoCVWrapper object>, propensity_model_final=None, model_Y_final=None, categories='auto', n_jobs=-1, backend='loky', verbose=3, batch_size='auto', random_state=None)[source]

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

Methods

 __init__(*[, n_trees, min_leaf_size, …]) 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]) Public interface for getting feature names. cate_output_names([output_names]) Public interface for getting output names. cate_treatment_names([treatment_names]) Get treatment names. 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 θ(·) conditional on a vector of features X. Inference results for the quantities $$\theta(X)$$ produced by the model. const_marginal_effect_interval([X, alpha]) Confidence intervals for the quantities $$\theta(X)$$ produced by the model. effect([X, T0, T1]) Calculate the heterogeneous treatment effect $$\tau(X, T0, T1)$$. effect_inference([X, T0, T1]) Inference results for the quantities $$\tau(X, T0, T1)$$ produced by the model. effect_interval([X, T0, T1, alpha]) Confidence intervals for the quantities $$\tau(X, T0, T1)$$ produced by the model. fit(Y, T, X[, W, inference]) Build an orthogonal random forest from a training set (Y, T, X, W). 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. Calculate the moments and mean gradient at points given by (Y, T, X, W). Generate nuissance estimator given model inputs from the class. parameter_estimator_func(Y, T, X, …[, …]) Calculate the parameter of interest for points given by (Y, T) and corresponding nuisance estimates. second_stage_parameter_estimator_gen(lambda_reg) For the second stage parameter estimation we add a local linear correction. shap_values(X, *[, feature_names, …]) Shap value for the final stage models (const_marginal_effect)

Attributes

 dowhy Get an instance of DoWhyWrapper to allow other functionalities from dowhy package. transformer
ate(X=None, *, T0=0, T1=1)

Calculate the average treatment effect $$E_X[\tau(X, T0, T1)]$$.

The effect is calculated between the two treatment points and is averaged over the population of X variables.

Parameters
• T0 ((m, d_t) matrix or vector of length m) – Base treatments for each sample

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

• X (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)

Public interface for getting feature names.

To be overriden by estimators that apply transformations the input features.

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 – Returns feature names.

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)[source]

Calculate the constant marginal CATE θ(·) conditional on a vector of features X.

Parameters

X (array-like, shape (n, d_x)) – Feature vector that captures heterogeneity.

Returns

Theta – Constant marginal CATE of each treatment for each sample.

Return type

matrix , shape (n, d_t)

const_marginal_effect_inference(X=None)

Inference results for the quantities $$\theta(X)$$ produced by the model. Available only when inference is not None, when calling the fit method.

Parameters

X (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, X, W=None, *, inference='auto')[source]

Build an orthogonal random forest from a training set (Y, T, X, W).

Parameters
• Y (array-like, shape (n, )) – Outcome for the treatment policy. Must be a vector.

• T (array-like, shape (n, )) – Discrete treatment policy vector. The treatment policy should be a set of consecutive integers starting with 0, where 0 denotes the control group. Otherwise, the treatment policies will be ordered lexicographically, with the smallest value being considered the control group.

• X (array-like, shape (n, d_x)) – Feature vector that captures heterogeneity.

• W (array-like, shape (n, d_w) or None (default=None)) – High-dimensional controls.

• inference (string, Inference instance, or None) – Method for performing inference. This estimator supports ‘bootstrap’ (or an instance of BootstrapInference) and ‘blb’ (or an instance of BLBInference)

Returns

self

Return type

an instance of self.

marginal_ate(T, X=None)

Calculate the average marginal effect $$E_{T, X}[\partial\tau(T, X)]$$.

The marginal effect is calculated around a base treatment point and averaged over the population of X.

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

• X (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) )

static moment_and_mean_gradient_estimator_func(Y, T, X, W, nuisance_estimates, parameter_estimate)[source]

Calculate the moments and mean gradient at points given by (Y, T, X, W).

static nuisance_estimator_generator(propensity_model, model_Y, random_state=None, second_stage=False)[source]

Generate nuissance estimator given model inputs from the class.

static parameter_estimator_func(Y, T, X, nuisance_estimates, sample_weight=None)[source]

Calculate the parameter of interest for points given by (Y, T) and corresponding nuisance estimates.

static second_stage_parameter_estimator_gen(lambda_reg)[source]

For the second stage parameter estimation we add a local linear correction. So we fit a local linear function as opposed to a local constant function. We also penalize the linear part to reduce variance.

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