Synthetic Potential Outcomes and Causal Mixture Identifiability

• URL: http://arxiv.org/abs/2405.19225v4
• Date: Fri, 13 Dec 2024 06:58:47 GMT
• Title: Synthetic Potential Outcomes and Causal Mixture Identifiability
• Authors: Bijan Mazaheri, Chandler Squires, Caroline Uhler,
• Abstract summary: Heterogeneity can be resolved at multiple levels by grouping populations according to different notions of similarity.<n>This paper proposes grouping with respect to the causal response of an intervention or perturbation on the system.
• Score: 9.649642656207869
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by grouping populations according to different notions of similarity. This paper proposes grouping with respect to the causal response of an intervention or perturbation on the system. This definition is distinct from previous notions, such as similar covariate values (e.g. clustering) or similar correlations between covariates (e.g. Gaussian mixture models). To solve the problem, we ``synthetically sample'' from a counterfactual distribution using higher-order multi-linear moments of the observable data. To understand how these ``causal mixtures'' fit in with more classical notions, we develop a hierarchy of mixture identifiability.

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