Wasserstein Random Forests and Applications in Heterogeneous Treatment Effects

Qiming Du, Gérard Biau, Francois Petit, Raphaël Porcher
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1729-1737, 2021.

Abstract

We present new insights into causal inference in the context of Heterogeneous Treatment Effects by proposing natural variants of Random Forests to estimate the key conditional distributions. To achieve this, we recast Breiman’s original splitting criterion in terms of Wasserstein distances between empirical measures. This reformulation indicates that Random Forests are well adapted to estimate conditional distributions and provides a natural extension of the algorithm to multi- variate outputs. Following the philosophy of Breiman’s construction, we propose some variants of the splitting rule that are well-suited to the conditional distribution estimation problem. Some preliminary theoretical connections are established along with various numerical experiments, which show how our approach may help to conduct more transparent causal inference in complex situations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-du21a, title = { Wasserstein Random Forests and Applications in Heterogeneous Treatment Effects }, author = {Du, Qiming and Biau, G{\'e}rard and Petit, Francois and Porcher, Rapha{\"e}l}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1729--1737}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/du21a/du21a.pdf}, url = {https://proceedings.mlr.press/v130/du21a.html}, abstract = { We present new insights into causal inference in the context of Heterogeneous Treatment Effects by proposing natural variants of Random Forests to estimate the key conditional distributions. To achieve this, we recast Breiman’s original splitting criterion in terms of Wasserstein distances between empirical measures. This reformulation indicates that Random Forests are well adapted to estimate conditional distributions and provides a natural extension of the algorithm to multi- variate outputs. Following the philosophy of Breiman’s construction, we propose some variants of the splitting rule that are well-suited to the conditional distribution estimation problem. Some preliminary theoretical connections are established along with various numerical experiments, which show how our approach may help to conduct more transparent causal inference in complex situations. } }
Endnote
%0 Conference Paper %T Wasserstein Random Forests and Applications in Heterogeneous Treatment Effects %A Qiming Du %A Gérard Biau %A Francois Petit %A Raphaël Porcher %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-du21a %I PMLR %P 1729--1737 %U https://proceedings.mlr.press/v130/du21a.html %V 130 %X We present new insights into causal inference in the context of Heterogeneous Treatment Effects by proposing natural variants of Random Forests to estimate the key conditional distributions. To achieve this, we recast Breiman’s original splitting criterion in terms of Wasserstein distances between empirical measures. This reformulation indicates that Random Forests are well adapted to estimate conditional distributions and provides a natural extension of the algorithm to multi- variate outputs. Following the philosophy of Breiman’s construction, we propose some variants of the splitting rule that are well-suited to the conditional distribution estimation problem. Some preliminary theoretical connections are established along with various numerical experiments, which show how our approach may help to conduct more transparent causal inference in complex situations.
APA
Du, Q., Biau, G., Petit, F. & Porcher, R.. (2021). Wasserstein Random Forests and Applications in Heterogeneous Treatment Effects . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1729-1737 Available from https://proceedings.mlr.press/v130/du21a.html.

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