Covariate balancing using the integral probability metric for causal inference

Insung Kong, Yuha Park, Joonhyuk Jung, Kwonsang Lee, Yongdai Kim
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:17430-17461, 2023.

Abstract

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-kong23d, title = {Covariate balancing using the integral probability metric for causal inference}, author = {Kong, Insung and Park, Yuha and Jung, Joonhyuk and Lee, Kwonsang and Kim, Yongdai}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {17430--17461}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/kong23d/kong23d.pdf}, url = {https://proceedings.mlr.press/v202/kong23d.html}, abstract = {Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.} }
Endnote
%0 Conference Paper %T Covariate balancing using the integral probability metric for causal inference %A Insung Kong %A Yuha Park %A Joonhyuk Jung %A Kwonsang Lee %A Yongdai Kim %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-kong23d %I PMLR %P 17430--17461 %U https://proceedings.mlr.press/v202/kong23d.html %V 202 %X Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.
APA
Kong, I., Park, Y., Jung, J., Lee, K. & Kim, Y.. (2023). Covariate balancing using the integral probability metric for causal inference. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:17430-17461 Available from https://proceedings.mlr.press/v202/kong23d.html.

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