Causal Inference Through the Structural Causal Marginal Problem

Luigi Gresele, Julius Von Kügelgen, Jonas Kübler, Elke Kirschbaum, Bernhard Schölkopf, Dominik Janzing
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:7793-7824, 2022.

Abstract

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-gresele22a, title = {Causal Inference Through the Structural Causal Marginal Problem}, author = {Gresele, Luigi and K{\"u}gelgen, Julius Von and K{\"u}bler, Jonas and Kirschbaum, Elke and Sch{\"o}lkopf, Bernhard and Janzing, Dominik}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {7793--7824}, 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/gresele22a/gresele22a.pdf}, url = {https://proceedings.mlr.press/v162/gresele22a.html}, abstract = {We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.} }
Endnote
%0 Conference Paper %T Causal Inference Through the Structural Causal Marginal Problem %A Luigi Gresele %A Julius Von Kügelgen %A Jonas Kübler %A Elke Kirschbaum %A Bernhard Schölkopf %A Dominik Janzing %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-gresele22a %I PMLR %P 7793--7824 %U https://proceedings.mlr.press/v162/gresele22a.html %V 162 %X We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.
APA
Gresele, L., Kügelgen, J.V., Kübler, J., Kirschbaum, E., Schölkopf, B. & Janzing, D.. (2022). Causal Inference Through the Structural Causal Marginal Problem. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:7793-7824 Available from https://proceedings.mlr.press/v162/gresele22a.html.

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