# econml._ortho_learner¶

Orthogonal Machine Learning is a general approach to estimating causal models by formulating them as minimizers of some loss function that depends on auxiliary regression models that also need to be estimated from data. The class in this module implements the general logic in a very versatile way so that various child classes can simply instantiate the appropriate models and save a lot of code repetition.

References

Dylan Foster, Vasilis Syrgkanis (2019). Orthogonal Statistical Learning.

ACM Conference on Learning Theory. https://arxiv.org/abs/1901.09036

Xinkun Nie, Stefan Wager (2017). Quasi-Oracle Estimation of Heterogeneous Treatment Effects.

https://arxiv.org/abs/1712.04912

Chernozhukov et al. (2017). Double/debiased machine learning for treatment and structural parameters.

The Econometrics Journal. https://arxiv.org/abs/1608.00060

Functions

 _crossfit(model, folds, *args, **kwargs) General crossfit based calculation of nuisance parameters.

Classes

 CachedValues(nuisances, Y, T, X, W, Z, …) _OrthoLearner(*, discrete_treatment, …[, …]) Base class for all orthogonal learners.
class econml._ortho_learner.CachedValues(nuisances, Y, T, X, W, Z, sample_weight, freq_weight, sample_var, groups)

Bases: tuple

count(value, /)

Return number of occurrences of value.

index(value, start=0, stop=9223372036854775807, /)

Return first index of value.

Raises ValueError if the value is not present.

property T

Alias for field number 2

property W

Alias for field number 4

property X

Alias for field number 3

property Y

Alias for field number 1

property Z

Alias for field number 5

property freq_weight

Alias for field number 7

property groups

Alias for field number 9

property nuisances

Alias for field number 0

property sample_var

Alias for field number 8

property sample_weight

Alias for field number 6

class econml._ortho_learner._OrthoLearner(*, discrete_treatment, discrete_instrument, categories, cv, random_state, mc_iters=None, mc_agg='mean')[source]

Base class for all orthogonal learners. This class is a parent class to any method that has the following architecture:

1. The CATE $$\theta(X)$$ is the minimizer of some expected loss function

$\mathbb{E}[\ell(V; \theta(X), h(V))]$

where $$V$$ are all the random variables and h is a vector of nuisance functions. Alternatively, the class would also work if $$\theta(X)$$ is the solution to a set of moment equations that also depend on nuisance functions $$h$$.

2. To estimate $$\theta(X)$$ we first fit the h functions and calculate $$h(V_i)$$ for each sample $$i$$ in a crossfit manner:

• Let (F1_train, F1_test), …, (Fk_train, Fk_test) be any KFold partition of the data, where Ft_train, Ft_test are subsets of indices of the input samples and such that F1_train is disjoint from F1_test. The sets F1_test, …, Fk_test form an incomplete partition of all the input indices, i.e. they are be disjoint and their union could potentially be a subset of all input indices. For instance, in a time series split F0_train could be a prefix of the data and F0_test the suffix. Typically, these folds will be created by a KFold split, i.e. if S1, …, Sk is any partition of the data, then Ft_train is the set of all indices except St and Ft_test = St. If the union of the Ft_test is not all the data, then only the subset of the data in the union of the Ft_test sets will be used in the final stage.

• Then for each t in [1, …, k]

• Estimate a model $$\hat{h}_t$$ for $$h$$ using Ft_train

• Evaluate the learned $$\hat{h}_t$$ model on the data in Ft_test and use that value as the nuisance value/vector $$\hat{U}_i=\hat{h}(V_i)$$ for the indices i in Ft_test

3. Estimate the model for $$\theta(X)$$ by minimizing the empirical (regularized) plugin loss on the subset of indices for which we have a nuisance value, i.e. the union of {F1_test, …, Fk_test}:

$\mathbb{E}_n[\ell(V; \theta(X), \hat{h}(V))] = \frac{1}{n} \sum_{i=1}^n \ell(V_i; \theta(X_i), \hat{U}_i)$

The method is a bit more general in that the final step does not need to be a loss minimization step. The class takes as input a model for fitting an estimate of the nuisance h given a set of samples and predicting the value of the learned nuisance model on any other set of samples. It also takes as input a model for the final estimation, that takes as input the data and their associated estimated nuisance values from the first stage and fits a model for the CATE $$\theta(X)$$. Then at predict time, the final model given any set of samples of the X variable, returns the estimated $$\theta(X)$$.

The method essentially implements all the crossfit and plugin logic, so that any child classes need to only implement the appropriate model_nuisance and model_final and essentially nothing more. It also implements the basic preprocessing logic behind the expansion of discrete treatments into one-hot encodings.

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

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

• 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.

• cv (int, cross-validation generator or an iterable) – 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[Z, W, X], T) to generate the splits. If all Z, W, X are None, then we call split(ones((T.shape[0], 1)), T).

• 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.

• 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.

Examples

The example code below implements a very simple version of the double machine learning method on top of the _OrthoLearner class, for expository purposes. For a more elaborate implementation of a Double Machine Learning child class of the class _OrthoLearner check out DML and its child classes:

import numpy as np
from sklearn.linear_model import LinearRegression
from econml._ortho_learner import _OrthoLearner
class ModelNuisance:
def __init__(self, model_t, model_y):
self._model_t = model_t
self._model_y = model_y
def fit(self, Y, T, W=None):
self._model_t.fit(W, T)
self._model_y.fit(W, Y)
return self
def predict(self, Y, T, W=None):
return Y - self._model_y.predict(W), T - self._model_t.predict(W)
class ModelFinal:
def __init__(self):
return
def fit(self, Y, T, W=None, nuisances=None):
Y_res, T_res = nuisances
self.model = LinearRegression(fit_intercept=False).fit(T_res.reshape(-1, 1), Y_res)
return self
def predict(self, X=None):
return self.model.coef_[0]
def score(self, Y, T, W=None, nuisances=None):
Y_res, T_res = nuisances
return np.mean((Y_res - self.model.predict(T_res.reshape(-1, 1)))**2)
class OrthoLearner(_OrthoLearner):
def _gen_ortho_learner_model_nuisance(self):
return ModelNuisance(LinearRegression(), LinearRegression())
def _gen_ortho_learner_model_final(self):
return ModelFinal()
np.random.seed(123)
X = np.random.normal(size=(100, 3))
y = X[:, 0] + X[:, 1] + np.random.normal(0, 0.1, size=(100,))
est = OrthoLearner(cv=2, discrete_treatment=False, discrete_instrument=False,
categories='auto', random_state=None)
est.fit(y, X[:, 0], W=X[:, 1:])

>>> est.score_
0.00756830...
>>> est.const_marginal_effect()
1.02364992...
>>> est.effect()
array([1.023649...])
>>> est.effect(T0=0, T1=10)
array([10.236499...])
>>> est.score(y, X[:, 0], W=X[:, 1:])
0.00727995...
>>> est.ortho_learner_model_final_.model
LinearRegression(fit_intercept=False)
>>> est.ortho_learner_model_final_.model.coef_
array([1.023649...])


The following example shows how to do double machine learning with discrete treatments, using the _OrthoLearner:

class ModelNuisance:
def __init__(self, model_t, model_y):
self._model_t = model_t
self._model_y = model_y
def fit(self, Y, T, W=None):
self._model_t.fit(W, np.matmul(T, np.arange(1, T.shape[1]+1)))
self._model_y.fit(W, Y)
return self
def predict(self, Y, T, W=None):
return Y - self._model_y.predict(W), T - self._model_t.predict_proba(W)[:, 1:]
class ModelFinal:
def __init__(self):
return
def fit(self, Y, T, W=None, nuisances=None):
Y_res, T_res = nuisances
self.model = LinearRegression(fit_intercept=False).fit(T_res.reshape(-1, 1), Y_res)
return self
def predict(self):
# theta needs to be of dimension (1, d_t) if T is (n, d_t)
return np.array([[self.model.coef_[0]]])
def score(self, Y, T, W=None, nuisances=None):
Y_res, T_res = nuisances
return np.mean((Y_res - self.model.predict(T_res.reshape(-1, 1)))**2)
from sklearn.linear_model import LogisticRegression
class OrthoLearner(_OrthoLearner):
def _gen_ortho_learner_model_nuisance(self):
return ModelNuisance(LogisticRegression(solver='lbfgs'), LinearRegression())
def _gen_ortho_learner_model_final(self):
return ModelFinal()
np.random.seed(123)
W = np.random.normal(size=(100, 3))
import scipy.special
T = np.random.binomial(1, scipy.special.expit(W[:, 0]))
y = T + W[:, 0] + np.random.normal(0, 0.01, size=(100,))
est = OrthoLearner(cv=2, discrete_treatment=True, discrete_instrument=False,
categories='auto', random_state=None)
est.fit(y, T, W=W)

>>> est.score_
0.00673015...
>>> est.const_marginal_effect()
array([[1.008401...]])
>>> est.effect()
array([1.008401...])
>>> est.score(y, T, W=W)
0.00310431...
>>> est.ortho_learner_model_final_.model.coef_[0]
1.00840170...

models_nuisance_

A nested list of instances of the model_nuisance object. The number of sublist equals to the 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.

Type

nested list of objects of type(model_nuisance)

ortho_learner_model_final_

An instance of the model_final object that was fitted after calling fit.

Type

object of type(model_final)

score_

If the model_final has a score method, then score_ contains the outcome of the final model score when evaluated on the fitted nuisances from the first stage. Represents goodness of fit, of the final CATE model.

Type

float or array of floats

nuisance_scores_

The out-of-sample scores from training each nuisance model

Type

tuple of nested lists of floats or None

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=None)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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=None, W=None, Z=None, *, sample_weight=None, freq_weight=None, sample_var=None, groups=None, cache_values=False, inference=None, only_final=False, check_input=True)[source]

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

• 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

• Z (optional (n, d_z) matrix or None (Default=None)) – Instruments 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 the inputs and computed nuisances, 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).

• only_final (bool, defaul False) – Whether to fit the nuisance models or use the existing cached values Note. This parameter is only used internally by the refit method and should not be exposed publicly by overwrites of the fit method in public classes.

• check_input (bool, default True) – Whether to check if the input is valid Note. This parameter is only used internally by the refit method and should not be exposed publicly by overwrites of the fit method in public classes.

Returns

self

Return type

object

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)[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, Z=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 nuisance models created at fit time. It uses the mean prediction of the models fitted by the different crossfit folds under different iterations. Then calls the score function of the model_final and returns the calculated score. The model_final model must have a score method.

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

• 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

• Z (optional (n, d_z) matrix or None (Default=None)) – Instruments for each sample

• sample_weight (optional(n,) vector or None (Default=None)) – Weights for each samples

Returns

score – The score of the final CATE model on the new data. Same type as the return type of the model_final.score method.

Return type

float or (array of 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

econml._ortho_learner._crossfit(model, folds, *args, **kwargs)[source]

General crossfit based calculation of nuisance parameters.

Parameters
• model (object) – An object that supports fit and predict. Fit must accept all the args and the keyword arguments kwargs. Similarly predict must all accept all the args as arguments and kwards as keyword arguments. The fit function estimates a model of the nuisance function, based on the input data to fit. Predict evaluates the fitted nuisance function on the input data to predict.

• folds (list of tuples or None) – The crossfitting fold structure. Every entry in the list is a tuple whose first element are the training indices of the args and kwargs data and the second entry are the test indices. If the union of the test indices is not the full set of all indices, then the remaining nuisance parameters for the missing indices have value NaN. If folds is None, then cross fitting is not performed; all indices are used for both model fitting and prediction

• args (a sequence of (numpy matrices or None)) – Each matrix is a data variable whose first index corresponds to a sample

• kwargs (a sequence of key-value args, with values being (numpy matrices or None)) – Each keyword argument is of the form Var=x, with x a numpy array. Each of these arrays are data variables. The model fit and predict will be called with signature: model.fit(*args, **kwargs) and model.predict(*args, **kwargs). Key-value arguments that have value None, are ommitted from the two calls. So all the args and the non None kwargs variables must be part of the models signature.

Returns

• nuisances (tuple of numpy matrices) – Each entry in the tuple is a nuisance parameter matrix. Each row i-th in the matrix corresponds to the value of the nuisance parameter for the i-th input sample.

• model_list (list of objects of same type as input model) – The cloned and fitted models for each fold. Can be used for inspection of the variability of the fitted models across folds.

• fitted_inds (np array1d) – The indices of the arrays for which the nuisance value was calculated. This corresponds to the union of the indices of the test part of each fold in the input fold list.

• scores (tuple of list of float or None) – The out-of-sample model scores for each nuisance model

Examples

import numpy as np
from sklearn.model_selection import KFold
from sklearn.linear_model import Lasso
from econml._ortho_learner import _crossfit
class Wrapper:
def __init__(self, model):
self._model = model
def fit(self, X, y, W=None):
self._model.fit(X, y)
return self
def predict(self, X, y, W=None):
return self._model.predict(X)
np.random.seed(123)
X = np.random.normal(size=(5000, 3))
y = X[:, 0] + np.random.normal(size=(5000,))
folds = list(KFold(2).split(X, y))
model = Lasso(alpha=0.01)
nuisance, model_list, fitted_inds, scores = _crossfit(Wrapper(model), folds, X, y, W=y, Z=None)

>>> nuisance
(array([-1.105728... , -1.537566..., -2.451827... , ...,  1.106287...,
-1.829662..., -1.782273...]),)
>>> model_list
[<Wrapper object at 0x...>, <Wrapper object at 0x...>]
>>> fitted_inds
array([   0,    1,    2, ..., 4997, 4998, 4999])