Bijan Mazaheri: Synthetic Potential Outcomes and the Hierarchy of Causal Identifiability

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Speaker: Bijan Mazaheri (Broad Institute of MIT and Harvard)
Title: Synthetic Potential Outcomes and the Hierarchy of Causal Identifiability
Abstract: A mixture model consists of a latent class that exerts a discrete signal on the observed data. Uncovering these latent classes is fundamental to unsupervised learning and forms the backbone of scientific thought. In this talk, we consider the problem of recovering latent classes of causal responses to an intervention. We allow overlapping support in the distributions of these classes, meaning individuals cannot be clustered into groups with a similar response. Instead, we develop a method of moments approach to synthetically sample potential outcome distributions using the higher-order multi-linear moments of the observable data. This approach is the first known identifiability result for what we call Mixtures of Treatment Effects (MTEs). More broadly, we show how MTEs fit into a hierarchy of mixture identifiability that unifies a number of previous approaches to latent class confounding.