Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models

Álvaro Ribot, Chandler Squires, Caroline Uhler
Proceedings of the Third Conference on Causal Learning and Reasoning, PMLR 236:1141-1175, 2024.

Abstract

We consider the task of causal imputation, where we aim to predict the outcomes of some set of actions across a wide range of possible contexts. As a running example, we consider predicting how different drugs affect cells from different cell types. We study the index-only setting, where the actions and contexts are categorical variables with a finite number of possible values. Even in this simple setting, a practical challenge arises, since often only a small subset of possible action-context pairs have been studied. Thus, models must extrapolate to novel action-context pairs, which can be framed as a form of matrix completion with rows indexed by actions, columns indexed by contexts, and matrix entries corresponding to outcomes. We introduce a novel SCM-based model class, where the outcome is expressed as a counterfactual, actions are expressed as interventions on an instrumental variable, and contexts are defined based on the initial state of the system. We show that, under a linearity assumption, this setup induces a latent factor model over the matrix of outcomes, with an additional fixed effect term. To perform causal prediction based on this model class, we introduce simple extension to the Synthetic Interventions estimator (Agarwal et al., 2020). We evaluate several matrix completion approaches on the PRISM drug repurposing dataset, showing that our method outperforms all other considered matrix completion approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v236-ribot24a, title = {Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models}, author = {Ribot, \'Alvaro and Squires, Chandler and Uhler, Caroline}, booktitle = {Proceedings of the Third Conference on Causal Learning and Reasoning}, pages = {1141--1175}, year = {2024}, editor = {Locatello, Francesco and Didelez, Vanessa}, volume = {236}, series = {Proceedings of Machine Learning Research}, month = {01--03 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v236/ribot24a/ribot24a.pdf}, url = {https://proceedings.mlr.press/v236/ribot24a.html}, abstract = {We consider the task of causal imputation, where we aim to predict the outcomes of some set of actions across a wide range of possible contexts. As a running example, we consider predicting how different drugs affect cells from different cell types. We study the index-only setting, where the actions and contexts are categorical variables with a finite number of possible values. Even in this simple setting, a practical challenge arises, since often only a small subset of possible action-context pairs have been studied. Thus, models must extrapolate to novel action-context pairs, which can be framed as a form of matrix completion with rows indexed by actions, columns indexed by contexts, and matrix entries corresponding to outcomes. We introduce a novel SCM-based model class, where the outcome is expressed as a counterfactual, actions are expressed as interventions on an instrumental variable, and contexts are defined based on the initial state of the system. We show that, under a linearity assumption, this setup induces a latent factor model over the matrix of outcomes, with an additional fixed effect term. To perform causal prediction based on this model class, we introduce simple extension to the Synthetic Interventions estimator (Agarwal et al., 2020). We evaluate several matrix completion approaches on the PRISM drug repurposing dataset, showing that our method outperforms all other considered matrix completion approaches.} }
Endnote
%0 Conference Paper %T Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models %A Álvaro Ribot %A Chandler Squires %A Caroline Uhler %B Proceedings of the Third Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2024 %E Francesco Locatello %E Vanessa Didelez %F pmlr-v236-ribot24a %I PMLR %P 1141--1175 %U https://proceedings.mlr.press/v236/ribot24a.html %V 236 %X We consider the task of causal imputation, where we aim to predict the outcomes of some set of actions across a wide range of possible contexts. As a running example, we consider predicting how different drugs affect cells from different cell types. We study the index-only setting, where the actions and contexts are categorical variables with a finite number of possible values. Even in this simple setting, a practical challenge arises, since often only a small subset of possible action-context pairs have been studied. Thus, models must extrapolate to novel action-context pairs, which can be framed as a form of matrix completion with rows indexed by actions, columns indexed by contexts, and matrix entries corresponding to outcomes. We introduce a novel SCM-based model class, where the outcome is expressed as a counterfactual, actions are expressed as interventions on an instrumental variable, and contexts are defined based on the initial state of the system. We show that, under a linearity assumption, this setup induces a latent factor model over the matrix of outcomes, with an additional fixed effect term. To perform causal prediction based on this model class, we introduce simple extension to the Synthetic Interventions estimator (Agarwal et al., 2020). We evaluate several matrix completion approaches on the PRISM drug repurposing dataset, showing that our method outperforms all other considered matrix completion approaches.
APA
Ribot, Á., Squires, C. & Uhler, C.. (2024). Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models. Proceedings of the Third Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 236:1141-1175 Available from https://proceedings.mlr.press/v236/ribot24a.html.

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