# Copyright (c) PyWhy contributors. All rights reserved.
# Licensed under the MIT License.
"""
The R Learner is an approach for estimating flexible non-parametric models
of conditional average treatment effects in the setting with no unobserved confounders.
The method is based on the idea of Neyman orthogonality and estimates a CATE
whose mean squared error is robust to the estimation errors of auxiliary submodels
that also need to be estimated from data:
1) the outcome or regression model
2) the treatment or propensity or policy or logging policy model
References
----------
Xinkun Nie, Stefan Wager (2017). Quasi-Oracle Estimation of Heterogeneous Treatment Effects.
https://arxiv.org/abs/1712.04912
Dylan Foster, Vasilis Syrgkanis (2019). Orthogonal Statistical Learning.
ACM Conference on Learning Theory. https://arxiv.org/abs/1901.09036
Chernozhukov et al. (2017). Double/debiased machine learning for treatment and structural parameters.
The Econometrics Journal. https://arxiv.org/abs/1608.00060
"""
from abc import abstractmethod
import numpy as np
import copy
from warnings import warn
from ..sklearn_extensions.model_selection import ModelSelector
from ..utilities import (shape, reshape, ndim, hstack, filter_none_kwargs, _deprecate_positional)
from sklearn.linear_model import LinearRegression
from sklearn.base import clone
from .._ortho_learner import _OrthoLearner
class _ModelNuisance(ModelSelector):
"""
Nuisance model fits the model_y and model_t at fit time and at predict time
calculates the residual Y and residual T based on the fitted models and returns
the residuals as two nuisance parameters.
"""
def __init__(self, model_y: ModelSelector, model_t: ModelSelector):
self._model_y = model_y
self._model_t = model_t
def train(self, is_selecting, folds, Y, T, X=None, W=None, Z=None, sample_weight=None, groups=None):
assert Z is None, "Cannot accept instrument!"
self._model_t.train(is_selecting, folds, X, W, T, **
filter_none_kwargs(sample_weight=sample_weight, groups=groups))
self._model_y.train(is_selecting, folds, X, W, Y, **
filter_none_kwargs(sample_weight=sample_weight, groups=groups))
return self
def score(self, Y, T, X=None, W=None, Z=None, sample_weight=None, groups=None):
# note that groups are not passed to score because they are only used for fitting
T_score = self._model_t.score(X, W, T, **filter_none_kwargs(sample_weight=sample_weight))
Y_score = self._model_y.score(X, W, Y, **filter_none_kwargs(sample_weight=sample_weight))
return Y_score, T_score
def predict(self, Y, T, X=None, W=None, Z=None, sample_weight=None, groups=None):
Y_pred = self._model_y.predict(X, W)
T_pred = self._model_t.predict(X, W)
if (X is None) and (W is None): # In this case predict above returns a single row
Y_pred = np.tile(Y_pred.reshape(1, -1), (Y.shape[0], 1))
T_pred = np.tile(T_pred.reshape(1, -1), (T.shape[0], 1))
Y_res = Y - Y_pred.reshape(Y.shape)
T_res = T - T_pred.reshape(T.shape)
return Y_res, T_res
@property
def needs_fit(self):
return self._model_y.needs_fit or self._model_t.needs_fit
class _ModelFinal:
"""
Final model at fit time, fits a residual on residual regression with a heterogeneous coefficient
that depends on X, i.e.
.. math ::
Y - E[Y | X, W] = \\theta(X) \\cdot (T - E[T | X, W]) + \\epsilon
and at predict time returns :math:`\\theta(X)`. The score method returns the MSE of this final
residual on residual regression.
"""
def __init__(self, model_final):
self._model_final = model_final
def fit(self, Y, T, X=None, W=None, Z=None, nuisances=None,
sample_weight=None, freq_weight=None, sample_var=None, groups=None):
Y_res, T_res = nuisances
self._model_final.fit(X, T, T_res, Y_res, sample_weight=sample_weight,
freq_weight=freq_weight, sample_var=sample_var)
return self
def predict(self, X=None):
return self._model_final.predict(X)
def score(self, Y, T, X=None, W=None, Z=None, nuisances=None, sample_weight=None, groups=None):
Y_res, T_res = nuisances
if Y_res.ndim == 1:
Y_res = Y_res.reshape((-1, 1))
if T_res.ndim == 1:
T_res = T_res.reshape((-1, 1))
effects = self._model_final.predict(X).reshape((-1, Y_res.shape[1], T_res.shape[1]))
Y_res_pred = np.einsum('ijk,ik->ij', effects, T_res).reshape(Y_res.shape)
if sample_weight is not None:
return np.mean(np.average((Y_res - Y_res_pred) ** 2, weights=sample_weight, axis=0))
else:
return np.mean((Y_res - Y_res_pred) ** 2)
[docs]class _RLearner(_OrthoLearner):
"""
Base class for CATE learners that residualize treatment and outcome and run residual on residual regression.
The estimator is a special of an :class:`._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
:class:`._OrthoLearner` for a description of this two stage process.
In this estimator, the CATE is estimated by using the following estimating equations:
.. math ::
Y - \\E[Y | X, W] = \\Theta(X) \\cdot (T - \\E[T | X, W]) + \\epsilon
Thus if we estimate the nuisance functions :math:`q(X, W) = \\E[Y | X, W]` and
:math:`f(X, W)=\\E[T | X, W]` in the first stage, we can estimate the final stage cate for each
treatment t, by running a regression, minimizing the residual on residual square loss:
.. math ::
\\hat{\\theta} = \\arg\\min_{\\Theta}\
\\E_n\\left[ (\\tilde{Y} - \\Theta(X) \\cdot \\tilde{T})^2 \\right]
Where :math:`\\tilde{Y}=Y - \\E[Y | X, W]` and :math:`\\tilde{T}=T-\\E[T | X, W]` denotes the
residual outcome and residual treatment.
Parameters
----------
discrete_outcome: bool
Whether the outcome should be treated as binary
discrete_treatment: bool
Whether the treatment values should be treated as categorical, rather than continuous, quantities
treatment_featurizer : :term:`transformer` or None
Must support fit_transform and transform. Used to create composite treatment in the final CATE regression.
The final CATE will be trained on the outcome of featurizer.fit_transform(T).
If featurizer=None, then CATE is trained on T.
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.
- :term:`CV splitter`
- An iterable yielding (train, test) splits as arrays of indices.
For integer/None inputs, if the treatment is discrete
:class:`~sklearn.model_selection.StratifiedKFold` is used, else,
:class:`~sklearn.model_selection.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)`.
random_state: int, :class:`~numpy.random.mtrand.RandomState` instance or None
If int, random_state is the seed used by the random number generator;
If :class:`~numpy.random.mtrand.RandomState` instance, random_state is the random number generator;
If None, the random number generator is the :class:`~numpy.random.mtrand.RandomState` instance used
by :mod:`np.random<numpy.random>`.
mc_iters: int, optional
The number of times to rerun the first stage models to reduce the variance of the nuisances.
mc_agg: {'mean', 'median'}, default 'mean'
How to aggregate the nuisance value for each sample across the `mc_iters` monte carlo iterations of
cross-fitting.
allow_missing: bool
Whether to allow missing values in X, W. If True, will need to supply nuisance models that can handle
missing values.
use_ray: bool, default False
Whether to use Ray to speed up the cross-fitting step.
ray_remote_func_options : dict, optional
Options to pass to ray.remote function decorator.
see more at https://docs.ray.io/en/latest/ray-core/api/doc/ray.remote.html
Examples
--------
The example code below implements a very simple version of the double machine learning
method on top of the :class:`._RLearner` class, for expository purposes.
For a more elaborate implementation of a Double Machine Learning child class of the class
checkout :class:`.DML` and its child classes:
.. testcode::
import numpy as np
from sklearn.linear_model import LinearRegression
from econml.dml._rlearner import _RLearner
from econml.sklearn_extensions.model_selection import SingleModelSelector
from sklearn.base import clone
class ModelFirst:
def __init__(self, model):
self._model = clone(model, safe=False)
def fit(self, X, W, Y, sample_weight=None):
self._model.fit(np.hstack([X, W]), Y)
return self
def predict(self, X, W):
return self._model.predict(np.hstack([X, W]))
class ModelSelector(SingleModelSelector):
def __init__(self, model):
self._model = ModelFirst(model)
def train(self, is_selecting, folds, X, W, Y, sample_weight=None):
self._model.fit(X, W, Y, sample_weight=sample_weight)
return self
@property
def best_model(self):
return self._model
@property
def best_score(self):
return 0
@property
def needs_fit(self):
return False
class ModelFinal:
def fit(self, X, T, T_res, Y_res, sample_weight=None, freq_weight=None, sample_var=None):
self.model = LinearRegression(fit_intercept=False).fit(X * T_res.reshape(-1, 1),
Y_res)
return self
def predict(self, X):
return self.model.predict(X)
class RLearner(_RLearner):
def _gen_model_y(self):
return ModelSelector(LinearRegression())
def _gen_model_t(self):
return ModelSelector(LinearRegression())
def _gen_rlearner_model_final(self):
return ModelFinal()
np.random.seed(123)
X = np.random.normal(size=(1000, 3))
y = X[:, 0] + X[:, 1] + np.random.normal(0, 0.01, size=(1000,))
est = RLearner(cv=2, discrete_outcome=False, discrete_treatment=False,
treatment_featurizer=None, categories='auto', random_state=None)
est.fit(y, X[:, 0], X=np.ones((X.shape[0], 1)), W=X[:, 1:])
>>> est.const_marginal_effect(np.ones((1,1)))
array([0.999631...])
>>> est.effect(np.ones((1,1)), T0=0, T1=10)
array([9.996314...])
>>> est.score(y, X[:, 0], X=np.ones((X.shape[0], 1)), W=X[:, 1:])
9.73638006...e-05
>>> est.rlearner_model_final_.model
LinearRegression(fit_intercept=False)
>>> est.rlearner_model_final_.model.coef_
array([0.999631...])
>>> est.score_
9.82623204...e-05
>>> [mdl._model for mdls in est.models_y for mdl in mdls]
[LinearRegression(), LinearRegression()]
>>> [mdl._model for mdls in est.models_t for mdl in mdls]
[LinearRegression(), LinearRegression()]
Attributes
----------
models_y: nested list of objects of type(model_y)
A nested list of instances of the model_y 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.
models_t: nested list of objects of type(model_t)
A nested list of instances of the model_t 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.
rlearner_model_final_ : object of type(model_final)
An instance of the model_final object that was fitted after calling fit.
score_ : float
The MSE in the final residual on residual regression
nuisance_scores_y : nested list of float
The out-of-sample scores for each outcome model
nuisance_scores_t : nested list of float
The out-of-sample scores for each treatment model
.. math::
\\frac{1}{n} \\sum_{i=1}^n (Y_i - \\hat{E}[Y|X_i, W_i]\
- \\hat{\\theta}(X_i)\\cdot (T_i - \\hat{E}[T|X_i, W_i]))^2
If `sample_weight` is not None at fit time, then a weighted average is returned. If the outcome Y
is multidimensional, then the average of the MSEs for each dimension of Y is returned.
"""
def __init__(self,
*,
discrete_outcome,
discrete_treatment,
treatment_featurizer,
categories,
cv,
random_state,
mc_iters=None,
mc_agg='mean',
allow_missing=False,
use_ray=False,
ray_remote_func_options=None):
super().__init__(discrete_outcome=discrete_outcome,
discrete_treatment=discrete_treatment,
treatment_featurizer=treatment_featurizer,
discrete_instrument=False, # no instrument, so doesn't matter
categories=categories,
cv=cv,
random_state=random_state,
mc_iters=mc_iters,
mc_agg=mc_agg,
allow_missing=allow_missing,
use_ray=use_ray,
ray_remote_func_options=ray_remote_func_options)
@abstractmethod
def _gen_model_y(self):
"""
Returns
-------
model_y: selector for the estimator of E[Y | X, W]
The estimator for fitting the response to the features and controls. Must implement
`fit` and `predict` methods. Unlike sklearn estimators both methods must
take an extra second argument (the controls), i.e. ::
model_y.fit(X, W, Y, sample_weight=sample_weight)
model_y.predict(X, W)
"""
raise NotImplementedError("Abstract method")
@abstractmethod
def _gen_model_t(self):
"""
Returns
-------
model_t: selector for the estimator of E[T | X, W]
The estimator for fitting the treatment to the features and controls. Must implement
`fit` and `predict` methods. Unlike sklearn estimators both methods must
take an extra second argument (the controls), i.e. ::
model_t.fit(X, W, T, sample_weight=sample_weight)
model_t.predict(X, W)
"""
raise NotImplementedError("Abstract method")
@abstractmethod
def _gen_rlearner_model_final(self):
"""
Returns
-------
model_final: estimator for fitting the response residuals to the features and treatment residuals
Must implement `fit` and `predict` methods. Unlike sklearn estimators the fit methods must
take an extra second argument (the treatment residuals). Predict, on the other hand,
should just take the features and return the constant marginal effect. More, concretely::
model_final.fit(X, T_res, Y_res,
sample_weight=sample_weight, freq_weight=freq_weight, sample_var=sample_var)
model_final.predict(X)
"""
raise NotImplementedError("Abstract method")
def _gen_ortho_learner_model_nuisance(self):
return _ModelNuisance(self._gen_model_y(), self._gen_model_t())
def _gen_ortho_learner_model_final(self):
return _ModelFinal(self._gen_rlearner_model_final())
[docs] def fit(self, Y, T, *, X=None, W=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 :math:`\\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:(n, d_x) matrix, optional
Features for each sample
W:(n, d_w) matrix, optional
Controls for each sample
sample_weight : (n,) array_like, optional
Individual weights for each sample. If None, it assumes equal weight.
freq_weight: (n, ) array_like of int, optional
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, optional
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: str, :class:`.Inference` instance, or None
Method for performing inference. This estimator supports 'bootstrap'
(or an instance of:class:`.BootstrapInference`).
Returns
-------
self: _RLearner instance
"""
# Replacing fit from _OrthoLearner, to enforce Z=None and improve the docstring
return super().fit(Y, T, X=X, W=W,
sample_weight=sample_weight, freq_weight=freq_weight, sample_var=sample_var, groups=groups,
cache_values=cache_values,
inference=inference)
[docs] def score(self, Y, T, X=None, W=None, sample_weight=None):
"""
Score the fitted CATE model on a new data set. Generates nuisance parameters
for the new data set based on the fitted residual nuisance models created at fit time.
It uses the mean prediction of the models fitted by the different crossfit folds.
Then calculates the MSE of the final residual Y on residual T regression.
If model_final does not have a score method, then it raises an :exc:`.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:(n, d_x) matrix, optional
Features for each sample
W:(n, d_w) matrix, optional
Controls for each sample
sample_weight:(n,) vector, optional
Weights for each samples
Returns
-------
score: float
The MSE of the final CATE model on the new data.
"""
# Replacing score from _OrthoLearner, to enforce Z=None and improve the docstring
return super().score(Y, T, X=X, W=W, sample_weight=sample_weight)
@property
def rlearner_model_final_(self):
# NOTE: important to get parent's wrapped copy so that
# after training wrapped featurizer is also trained, etc.
return self.ortho_learner_model_final_._model_final
@property
def models_y(self):
return [[mdl._model_y.best_model for mdl in mdls] for mdls in super().models_nuisance_]
@property
def models_t(self):
return [[mdl._model_t.best_model for mdl in mdls] for mdls in super().models_nuisance_]
@property
def nuisance_scores_y(self):
return self.nuisance_scores_[0]
@property
def nuisance_scores_t(self):
return self.nuisance_scores_[1]
@property
def residuals_(self):
"""
A tuple (y_res, T_res, X, W), of the residuals from the first stage estimation
along with the associated X and W. Samples are not guaranteed to be in the same
order as the input order.
"""
if not hasattr(self, '_cached_values'):
raise AttributeError("Estimator is not fitted yet!")
if self._cached_values is None:
raise AttributeError("`fit` was called with `cache_values=False`. "
"Set to `True` to enable residual storage.")
Y_res, T_res = self._cached_values.nuisances
return Y_res, T_res, self._cached_values.X, self._cached_values.W