Awesome
EconML is a Python package for estimating heterogeneous treatment effects from observational data via machine learning. This package was designed and built as part of the ALICE project at Microsoft Research with the goal to combine state-of-the-art machine learning techniques with econometrics to bring automation to complex causal inference problems. The promise of EconML:
- Implement recent techniques in the literature at the intersection of econometrics and machine learning
- Maintain flexibility in modeling the effect heterogeneity (via techniques such as random forests, boosting, lasso and neural nets), while preserving the causal interpretation of the learned model and often offering valid confidence intervals
- Use a unified API
- Build on standard Python packages for Machine Learning and Data Analysis
One of the biggest promises of machine learning is to automate decision making in a multitude of domains. At the core of many data-driven personalized decision scenarios is the estimation of heterogeneous treatment effects: what is the causal effect of an intervention on an outcome of interest for a sample with a particular set of features? In a nutshell, this toolkit is designed to measure the causal effect of some treatment variable(s) T on an outcome
variable Y, controlling for a set of features X, W and how does that effect vary as a function of X. The methods implemented are applicable even with observational (non-experimental or historical) datasets. For the estimation results to have a causal interpretation, some methods assume no unobserved confounders (i.e. there is no unobserved variable not included in X, W that simultaneously has an effect on both T and Y), while others assume access to an instrument Z (i.e. an observed variable Z that has an effect on the treatment T but no direct effect on the outcome Y). Most methods provide confidence intervals and inference results.
For detailed information about the package, consult the documentation at https://econml.azurewebsites.net/.
For information on use cases and background material on causal inference and heterogeneous treatment effects see our webpage at https://www.microsoft.com/en-us/research/project/econml/
<details> <summary><strong><em>Table of Contents</em></strong></summary>- News
- Getting Started
- For Developers
- Blogs and Publications
- Citation
- Contributing and Feedback
- Community
- References
News
If you'd like to contribute to this project, see the Help Wanted section below.
July 3, 2024: Release v0.15.1, see release notes here
<details><summary>Previous releases</summary>February 12, 2024: Release v0.15.0, see release notes here
November 11, 2023: Release v0.15.0b1, see release notes here
May 19, 2023: Release v0.14.1, see release notes here
November 16, 2022: Release v0.14.0, see release notes here
June 17, 2022: Release v0.13.1, see release notes here
January 31, 2022: Release v0.13.0, see release notes here
August 13, 2021: Release v0.12.0, see release notes here
August 5, 2021: Release v0.12.0b6, see release notes here
August 3, 2021: Release v0.12.0b5, see release notes here
July 9, 2021: Release v0.12.0b4, see release notes here
June 25, 2021: Release v0.12.0b3, see release notes here
June 18, 2021: Release v0.12.0b2, see release notes here
June 7, 2021: Release v0.12.0b1, see release notes here
May 18, 2021: Release v0.11.1, see release notes here
May 8, 2021: Release v0.11.0, see release notes here
March 22, 2021: Release v0.10.0, see release notes here
March 11, 2021: Release v0.9.2, see release notes here
March 3, 2021: Release v0.9.1, see release notes here
February 20, 2021: Release v0.9.0, see release notes here
January 20, 2021: Release v0.9.0b1, see release notes here
November 20, 2020: Release v0.8.1, see release notes here
November 18, 2020: Release v0.8.0, see release notes here
September 4, 2020: Release v0.8.0b1, see release notes here
March 6, 2020: Release v0.7.0, see release notes here
February 18, 2020: Release v0.7.0b1, see release notes here
January 10, 2020: Release v0.6.1, see release notes here
December 6, 2019: Release v0.6, see release notes here
November 21, 2019: Release v0.5, see release notes here.
June 3, 2019: Release v0.4, see release notes here.
May 3, 2019: Release v0.3, see release notes here.
April 10, 2019: Release v0.2, see release notes here.
March 6, 2019: Release v0.1, welcome to have a try and provide feedback.
</details>Getting Started
Installation
Install the latest release from PyPI:
pip install econml
To install from source, see For Developers section below.
Usage Examples
Estimation Methods
<details> <summary>Double Machine Learning (aka RLearner) (click to expand)</summary>- Linear final stage
from econml.dml import LinearDML
from sklearn.linear_model import LassoCV
from econml.inference import BootstrapInference
est = LinearDML(model_y=LassoCV(), model_t=LassoCV())
### Estimate with OLS confidence intervals
est.fit(Y, T, X=X, W=W) # W -> high-dimensional confounders, X -> features
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05) # OLS confidence intervals
### Estimate with bootstrap confidence intervals
est.fit(Y, T, X=X, W=W, inference='bootstrap') # with default bootstrap parameters
est.fit(Y, T, X=X, W=W, inference=BootstrapInference(n_bootstrap_samples=100)) # or customized
lb, ub = est.effect_interval(X_test, alpha=0.05) # Bootstrap confidence intervals
- Sparse linear final stage
from econml.dml import SparseLinearDML
from sklearn.linear_model import LassoCV
est = SparseLinearDML(model_y=LassoCV(), model_t=LassoCV())
est.fit(Y, T, X=X, W=W) # X -> high dimensional features
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05) # Confidence intervals via debiased lasso
- Generic Machine Learning last stage
from econml.dml import NonParamDML
from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier
est = NonParamDML(model_y=RandomForestRegressor(),
model_t=RandomForestClassifier(),
model_final=RandomForestRegressor(),
discrete_treatment=True)
est.fit(Y, T, X=X, W=W)
treatment_effects = est.effect(X_test)
from econml.panel.dml import DynamicDML
# Use defaults
est = DynamicDML()
# Or specify hyperparameters
est = DynamicDML(model_y=LassoCV(cv=3),
model_t=LassoCV(cv=3),
cv=3)
est.fit(Y, T, X=X, W=None, groups=groups, inference="auto")
# Effects
treatment_effects = est.effect(X_test)
# Confidence intervals
lb, ub = est.effect_interval(X_test, alpha=0.05)
from econml.dml import CausalForestDML
from sklearn.linear_model import LassoCV
# Use defaults
est = CausalForestDML()
# Or specify hyperparameters
est = CausalForestDML(criterion='het', n_estimators=500,
min_samples_leaf=10,
max_depth=10, max_samples=0.5,
discrete_treatment=False,
model_t=LassoCV(), model_y=LassoCV())
est.fit(Y, T, X=X, W=W)
treatment_effects = est.effect(X_test)
# Confidence intervals via Bootstrap-of-Little-Bags for forests
lb, ub = est.effect_interval(X_test, alpha=0.05)
from econml.orf import DMLOrthoForest, DROrthoForest
from econml.sklearn_extensions.linear_model import WeightedLasso, WeightedLassoCV
# Use defaults
est = DMLOrthoForest()
est = DROrthoForest()
# Or specify hyperparameters
est = DMLOrthoForest(n_trees=500, min_leaf_size=10,
max_depth=10, subsample_ratio=0.7,
lambda_reg=0.01,
discrete_treatment=False,
model_T=WeightedLasso(alpha=0.01), model_Y=WeightedLasso(alpha=0.01),
model_T_final=WeightedLassoCV(cv=3), model_Y_final=WeightedLassoCV(cv=3))
est.fit(Y, T, X=X, W=W)
treatment_effects = est.effect(X_test)
# Confidence intervals via Bootstrap-of-Little-Bags for forests
lb, ub = est.effect_interval(X_test, alpha=0.05)
- XLearner
from econml.metalearners import XLearner
from sklearn.ensemble import GradientBoostingClassifier, GradientBoostingRegressor
est = XLearner(models=GradientBoostingRegressor(),
propensity_model=GradientBoostingClassifier(),
cate_models=GradientBoostingRegressor())
est.fit(Y, T, X=np.hstack([X, W]))
treatment_effects = est.effect(np.hstack([X_test, W_test]))
# Fit with bootstrap confidence interval construction enabled
est.fit(Y, T, X=np.hstack([X, W]), inference='bootstrap')
treatment_effects = est.effect(np.hstack([X_test, W_test]))
lb, ub = est.effect_interval(np.hstack([X_test, W_test]), alpha=0.05) # Bootstrap CIs
- SLearner
from econml.metalearners import SLearner
from sklearn.ensemble import GradientBoostingRegressor
est = SLearner(overall_model=GradientBoostingRegressor())
est.fit(Y, T, X=np.hstack([X, W]))
treatment_effects = est.effect(np.hstack([X_test, W_test]))
- TLearner
from econml.metalearners import TLearner
from sklearn.ensemble import GradientBoostingRegressor
est = TLearner(models=GradientBoostingRegressor())
est.fit(Y, T, X=np.hstack([X, W]))
treatment_effects = est.effect(np.hstack([X_test, W_test]))
- Linear final stage
from econml.dr import LinearDRLearner
from sklearn.ensemble import GradientBoostingRegressor, GradientBoostingClassifier
est = LinearDRLearner(model_propensity=GradientBoostingClassifier(),
model_regression=GradientBoostingRegressor())
est.fit(Y, T, X=X, W=W)
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05)
- Sparse linear final stage
from econml.dr import SparseLinearDRLearner
from sklearn.ensemble import GradientBoostingRegressor, GradientBoostingClassifier
est = SparseLinearDRLearner(model_propensity=GradientBoostingClassifier(),
model_regression=GradientBoostingRegressor())
est.fit(Y, T, X=X, W=W)
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05)
- Nonparametric final stage
from econml.dr import ForestDRLearner
from sklearn.ensemble import GradientBoostingRegressor, GradientBoostingClassifier
est = ForestDRLearner(model_propensity=GradientBoostingClassifier(),
model_regression=GradientBoostingRegressor())
est.fit(Y, T, X=X, W=W)
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05)
- Orthogonal instrumental variable learner
from econml.iv.dml import OrthoIV
est = OrthoIV(projection=False,
discrete_treatment=True,
discrete_instrument=True)
est.fit(Y, T, Z=Z, X=X, W=W)
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05) # OLS confidence intervals
- Nonparametric double machine learning with instrumental variable
from econml.iv.dml import NonParamDMLIV
est = NonParamDMLIV(projection=False,
discrete_treatment=True,
discrete_instrument=True)
est.fit(Y, T, Z=Z, X=X, W=W) # no analytical confidence interval available
treatment_effects = est.effect(X_test)
- Linear final stage
from econml.iv.dr import LinearDRIV
est = LinearDRIV(discrete_instrument=True, discrete_treatment=True)
est.fit(Y, T, Z=Z, X=X, W=W)
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05) # OLS confidence intervals
- Sparse linear final stage
from econml.iv.dr import SparseLinearDRIV
est = SparseLinearDRIV(discrete_instrument=True, discrete_treatment=True)
est.fit(Y, T, Z=Z, X=X, W=W)
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05) # Debiased lasso confidence intervals
- Nonparametric final stage
from econml.iv.dr import ForestDRIV
est = ForestDRIV(discrete_instrument=True, discrete_treatment=True)
est.fit(Y, T, Z=Z, X=X, W=W)
treatment_effects = est.effect(X_test)
# Confidence intervals via Bootstrap-of-Little-Bags for forests
lb, ub = est.effect_interval(X_test, alpha=0.05)
- Linear intent-to-treat (discrete instrument, discrete treatment)
from econml.iv.dr import LinearIntentToTreatDRIV
from sklearn.ensemble import GradientBoostingRegressor, GradientBoostingClassifier
est = LinearIntentToTreatDRIV(model_y_xw=GradientBoostingRegressor(),
model_t_xwz=GradientBoostingClassifier(),
flexible_model_effect=GradientBoostingRegressor())
est.fit(Y, T, Z=Z, X=X, W=W)
treatment_effects = est.effect(X_test)
lb, ub = est.effect_interval(X_test, alpha=0.05) # OLS confidence intervals
import keras
from econml.iv.nnet import DeepIV
treatment_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(2,)),
keras.layers.Dropout(0.17),
keras.layers.Dense(64, activation='relu'),
keras.layers.Dropout(0.17),
keras.layers.Dense(32, activation='relu'),
keras.layers.Dropout(0.17)])
response_model = keras.Sequential([keras.layers.Dense(128, activation='relu', input_shape=(2,)),
keras.layers.Dropout(0.17),
keras.layers.Dense(64, activation='relu'),
keras.layers.Dropout(0.17),
keras.layers.Dense(32, activation='relu'),
keras.layers.Dropout(0.17),
keras.layers.Dense(1)])
est = DeepIV(n_components=10, # Number of gaussians in the mixture density networks)
m=lambda z, x: treatment_model(keras.layers.concatenate([z, x])), # Treatment model
h=lambda t, x: response_model(keras.layers.concatenate([t, x])), # Response model
n_samples=1 # Number of samples used to estimate the response
)
est.fit(Y, T, X=X, Z=Z) # Z -> instrumental variables
treatment_effects = est.effect(X_test)
See the <a href="#references">References</a> section for more details.
Interpretability
<details> <summary>Tree Interpreter of the CATE model (click to expand)</summary>from econml.cate_interpreter import SingleTreeCateInterpreter
intrp = SingleTreeCateInterpreter(include_model_uncertainty=True, max_depth=2, min_samples_leaf=10)
# We interpret the CATE model's behavior based on the features used for heterogeneity
intrp.interpret(est, X)
# Plot the tree
plt.figure(figsize=(25, 5))
intrp.plot(feature_names=['A', 'B', 'C', 'D'], fontsize=12)
plt.show()
from econml.cate_interpreter import SingleTreePolicyInterpreter
# We find a tree-based treatment policy based on the CATE model
intrp = SingleTreePolicyInterpreter(risk_level=0.05, max_depth=2, min_samples_leaf=1,min_impurity_decrease=.001)
intrp.interpret(est, X, sample_treatment_costs=0.2)
# Plot the tree
plt.figure(figsize=(25, 5))
intrp.plot(feature_names=['A', 'B', 'C', 'D'], fontsize=12)
plt.show()
import shap
from econml.dml import CausalForestDML
est = CausalForestDML()
est.fit(Y, T, X=X, W=W)
shap_values = est.shap_values(X)
shap.summary_plot(shap_values['Y0']['T0'])
Causal Model Selection and Cross-Validation
<details> <summary>Causal model selection with the `RScorer` (click to expand)</summary>from econml.score import RScorer
# split data in train-validation
X_train, X_val, T_train, T_val, Y_train, Y_val = train_test_split(X, T, y, test_size=.4)
# define list of CATE estimators to select among
reg = lambda: RandomForestRegressor(min_samples_leaf=20)
clf = lambda: RandomForestClassifier(min_samples_leaf=20)
models = [('ldml', LinearDML(model_y=reg(), model_t=clf(), discrete_treatment=True,
cv=3)),
('xlearner', XLearner(models=reg(), cate_models=reg(), propensity_model=clf())),
('dalearner', DomainAdaptationLearner(models=reg(), final_models=reg(), propensity_model=clf())),
('slearner', SLearner(overall_model=reg())),
('drlearner', DRLearner(model_propensity=clf(), model_regression=reg(),
model_final=reg(), cv=3)),
('rlearner', NonParamDML(model_y=reg(), model_t=clf(), model_final=reg(),
discrete_treatment=True, cv=3)),
('dml3dlasso', DML(model_y=reg(), model_t=clf(),
model_final=LassoCV(cv=3, fit_intercept=False),
discrete_treatment=True,
featurizer=PolynomialFeatures(degree=3),
cv=3))
]
# fit cate models on train data
models = [(name, mdl.fit(Y_train, T_train, X=X_train)) for name, mdl in models]
# score cate models on validation data
scorer = RScorer(model_y=reg(), model_t=clf(),
discrete_treatment=True, cv=3, mc_iters=2, mc_agg='median')
scorer.fit(Y_val, T_val, X=X_val)
rscore = [scorer.score(mdl) for _, mdl in models]
# select the best model
mdl, _ = scorer.best_model([mdl for _, mdl in models])
# create weighted ensemble model based on score performance
mdl, _ = scorer.ensemble([mdl for _, mdl in models])
EconML's cross-fitting estimators provide built-in functionality for first-stage model selection. This support can work with existing sklearn model selection classes such as LassoCV or GridSearchCV, or you can pass a list of models to choose the best from among them when cross-fitting.
from econml.dml import LinearDML
from sklearn import clone
from sklearn.ensemble import RandomForestRegressor
from sklearn.linear_model import LassoCV
from sklearn.model_selection import GridSearchCV
cv_model = GridSearchCV(
estimator=RandomForestRegressor(),
param_grid={
"max_depth": [3, None],
"n_estimators": (10, 30, 50, 100, 200),
"max_features": (2, 4, 6),
},
cv=5,
)
est = LinearDML(model_y=cv_model, # use sklearn's grid search to select the best Y model
model_t=[RandomForestRegressor(), LassoCV()]) # use built-in model selection to choose between forest and linear models for T model
Inference
Whenever inference is enabled, then one can get a more structure InferenceResults object with more elaborate inference information, such
as p-values and z-statistics. When the CATE model is linear and parametric, then a summary() method is also enabled. For instance:
from econml.dml import LinearDML
# Use defaults
est = LinearDML()
est.fit(Y, T, X=X, W=W)
# Get the effect inference summary, which includes the standard error, z test score, p value, and confidence interval given each sample X[i]
est.effect_inference(X_test).summary_frame(alpha=0.05, value=0, decimals=3)
# Get the population summary for the entire sample X
est.effect_inference(X_test).population_summary(alpha=0.1, value=0, decimals=3, tol=0.001)
# Get the parameter inference summary for the final model
est.summary()
# Get the effect inference summary, which includes the standard error, z test score, p value, and confidence interval given each sample X[i]
est.effect_inference(X_test).summary_frame(alpha=0.05, value=0, decimals=3)
# Get the population summary for the entire sample X
est.effect_inference(X_test).population_summary(alpha=0.1, value=0, decimals=3, tol=0.001)
# Get the parameter inference summary for the final model
est.summary()
Policy Learning
You can also perform direct policy learning from observational data, using the doubly robust method for offline policy learning. These methods directly predict a recommended treatment, without internally fitting an explicit model of the conditional average treatment effect.
<details> <summary>Doubly Robust Policy Learning (click to expand)</summary>from econml.policy import DRPolicyTree, DRPolicyForest
from sklearn.ensemble import RandomForestRegressor
# fit a single binary decision tree policy
policy = DRPolicyTree(max_depth=1, min_impurity_decrease=0.01, honest=True)
policy.fit(y, T, X=X, W=W)
# predict the recommended treatment
recommended_T = policy.predict(X)
# plot the binary decision tree
plt.figure(figsize=(10,5))
policy.plot()
# get feature importances
importances = policy.feature_importances_
# fit a binary decision forest
policy = DRPolicyForest(max_depth=1, min_impurity_decrease=0.01, honest=True)
policy.fit(y, T, X=X, W=W)
# predict the recommended treatment
recommended_T = policy.predict(X)
# plot the first tree in the ensemble
plt.figure(figsize=(10,5))
policy.plot(0)
# get feature importances
importances = policy.feature_importances_
To see more complex examples, go to the notebooks section of the repository. For a more detailed description of the treatment effect estimation algorithms, see the EconML documentation.
For Developers
You can get started by cloning this repository. We use
setuptools for building and distributing our package.
We rely on some recent features of setuptools, so make sure to upgrade to a recent version with
pip install setuptools --upgrade. Then from your local copy of the repository you can run pip install -e . to get started (but depending on what you're doing you might want to install with extras instead, like pip install -e .[plt] if you want to use matplotlib integration, or you can use pip install -e .[all] to include all extras).
Pre-commit hooks
We use the pre-commit framework to enforce code style and run checks before every commit. To install the pre-commit hooks, make sure you have pre-commit installed (pip install pre-commit) and then run pre-commit install in the root of the repository. This will install the hooks and run them automatically before every commit. If you want to run the hooks manually, you can run pre-commit run --all-files.
Finding issues to help with
If you're looking to contribute to the project, we have a number of issues tagged with the up for grabs and help wanted labels. "Up for grabs" issues are ones that we think that people without a lot of experience in our codebase may be able to help with, while "Help wanted" issues are valuable improvements to the library that our team currently does not have time to prioritize where we would greatly appreciate community-initiated PRs, but which might be more involved.
Running the tests
This project uses pytest to run tests for continuous integration. It is also possible to use pytest to run tests locally, but this isn't recommended because it will take an extremely long time and some tests are specific to certain environments or scenarios that have additional dependencies. However, if you'd like to do this anyway, to run all tests locally after installing the package you can use pip install pytest pytest-xdist pytest-cov coverage[toml] (as well as pip install jupyter jupyter-client nbconvert nbformat seaborn xgboost tqdm for the dependencies to run all of our notebooks as tests) followed by python -m pytest.
Because running all tests can be very time-consuming, we recommend running only the relevant subset of tests when developing locally. The easiest way to do this is to rely on pytest's compatibility with unittest, so you can just run python -m unittest econml.tests.test_module to run all tests in a given module, or python -m unittest econml.tests.test_module.TestClass to run all tests in a given class. You can also run python -m unittest econml.tests.test_module.TestClass.test_method to run a single test method.
Generating the documentation
This project's documentation is generated via Sphinx. Note that we use graphviz's
dot application to produce some of the images in our documentation, so you should make sure that dot is installed and in your path.
To generate a local copy of the documentation from a clone of this repository, just run python setup.py build_sphinx -W -E -a, which will build the documentation and place it under the build/sphinx/html path.
The reStructuredText files that make up the documentation are stored in the docs directory; module documentation is automatically generated by the Sphinx build process.
Release process
We use GitHub Actions to build and publish the package and documentation. To create a new release, an admin should perform the following steps:
- Update the version number in
econml/_version.pyand add a mention of the new version in the news section of this file and commit the changes. - Manually run the publish_package.yml workflow to build and publish the package to PyPI.
- Manually run the publish_docs.yml workflow to build and publish the documentation.
- Under https://github.com/py-why/EconML/releases, create a new release with a corresponding tag, and update the release notes.
Blogs and Publications
-
May 2021: Be Careful When Interpreting Predictive Models in Search of Causal Insights
-
June 2019: Treatment Effects with Instruments paper
-
May 2019: Open Data Science Conference Workshop
-
2017: DeepIV paper
Citation
If you use EconML in your research, please cite us as follows:
Keith Battocchi, Eleanor Dillon, Maggie Hei, Greg Lewis, Paul Oka, Miruna Oprescu, Vasilis Syrgkanis. EconML: A Python Package for ML-Based Heterogeneous Treatment Effects Estimation. https://github.com/py-why/EconML, 2019. Version 0.x.
BibTex:
@misc{econml,
author={Keith Battocchi, Eleanor Dillon, Maggie Hei, Greg Lewis, Paul Oka, Miruna Oprescu, Vasilis Syrgkanis},
title={{EconML}: {A Python Package for ML-Based Heterogeneous Treatment Effects Estimation}},
howpublished={https://github.com/py-why/EconML},
note={Version 0.x},
year={2019}
}
Contributing and Feedback
This project welcomes contributions and suggestions. We use the DCO bot to enforce a Developer Certificate of Origin which requires users to sign-off on their commits. This is a simple way to certify that you wrote or otherwise have the right to submit the code you are contributing to the project. Git provides a -s command line option to include this automatically when you commit via git commit.
When you submit a pull request, a CLA-bot will automatically determine whether you need to provide a CLA and decorate the PR appropriately (e.g., label, comment). Simply follow the instructions provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the PyWhy Code of Conduct.
Community
<a href="https://pywhy.org/"> <img src="doc/spec/img/pywhy-logo.png" width="80px" align="left" style="margin-right: 10px;", alt="pywhy-logo"> </a>EconML is a part of PyWhy, an organization with a mission to build an open-source ecosystem for causal machine learning.
PyWhy also has a Discord, which serves as a space for like-minded casual machine learning researchers and practitioners of all experience levels to come together to ask and answer questions, discuss new features, and share ideas.
We invite you to join us at regular office hours and community calls in the Discord.
References
Athey, Susan, and Stefan Wager. Policy learning with observational data. Econometrica 89.1, 133-161, 2021.
X Nie, S Wager. Quasi-Oracle Estimation of Heterogeneous Treatment Effects. Biometrika 108.2, 299-319, 2021.
V. Syrgkanis, V. Lei, M. Oprescu, M. Hei, K. Battocchi, G. Lewis. Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments. Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS), 2019. (Spotlight Presentation)
D. Foster, V. Syrgkanis. Orthogonal Statistical Learning. Proceedings of the 32nd Annual Conference on Learning Theory (COLT), 2019. (Best Paper Award)
M. Oprescu, V. Syrgkanis and Z. S. Wu. Orthogonal Random Forest for Causal Inference. Proceedings of the 36th International Conference on Machine Learning (ICML), 2019.
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