Partial Counterfactual Identification from Observational and Experimental Data

Junzhe Zhang, Jin Tian, Elias Bareinboim
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:26548-26558, 2022.

Abstract

This paper investigates the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form of a causal diagram. We show that all counterfactual distributions in an arbitrary structural causal model (SCM) with discrete observed domains could be generated by a canonical family of SCMs with the same causal diagram where unobserved (exogenous) variables are also discrete, taking values in finite domains. Utilizing the canonical SCMs, we translate the problem of bounding counterfactuals into that of polynomial programming whose solution provides optimal bounds for the counterfactual query. Solving such polynomial programs is in general computationally expensive. We then develop effective Monte Carlo algorithms to approximate optimal bounds from a combination of observational and experimental data. Our algorithms are validated extensively on synthetic and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-zhang22ab, title = {Partial Counterfactual Identification from Observational and Experimental Data}, author = {Zhang, Junzhe and Tian, Jin and Bareinboim, Elias}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {26548--26558}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/zhang22ab/zhang22ab.pdf}, url = {https://proceedings.mlr.press/v162/zhang22ab.html}, abstract = {This paper investigates the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form of a causal diagram. We show that all counterfactual distributions in an arbitrary structural causal model (SCM) with discrete observed domains could be generated by a canonical family of SCMs with the same causal diagram where unobserved (exogenous) variables are also discrete, taking values in finite domains. Utilizing the canonical SCMs, we translate the problem of bounding counterfactuals into that of polynomial programming whose solution provides optimal bounds for the counterfactual query. Solving such polynomial programs is in general computationally expensive. We then develop effective Monte Carlo algorithms to approximate optimal bounds from a combination of observational and experimental data. Our algorithms are validated extensively on synthetic and real-world datasets.} }
Endnote
%0 Conference Paper %T Partial Counterfactual Identification from Observational and Experimental Data %A Junzhe Zhang %A Jin Tian %A Elias Bareinboim %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-zhang22ab %I PMLR %P 26548--26558 %U https://proceedings.mlr.press/v162/zhang22ab.html %V 162 %X This paper investigates the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form of a causal diagram. We show that all counterfactual distributions in an arbitrary structural causal model (SCM) with discrete observed domains could be generated by a canonical family of SCMs with the same causal diagram where unobserved (exogenous) variables are also discrete, taking values in finite domains. Utilizing the canonical SCMs, we translate the problem of bounding counterfactuals into that of polynomial programming whose solution provides optimal bounds for the counterfactual query. Solving such polynomial programs is in general computationally expensive. We then develop effective Monte Carlo algorithms to approximate optimal bounds from a combination of observational and experimental data. Our algorithms are validated extensively on synthetic and real-world datasets.
APA
Zhang, J., Tian, J. & Bareinboim, E.. (2022). Partial Counterfactual Identification from Observational and Experimental Data. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:26548-26558 Available from https://proceedings.mlr.press/v162/zhang22ab.html.

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