Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models
This addresses the challenge of extrapolating to unobserved drug-cell combinations in biomedical research, representing an incremental improvement over existing matrix completion methods.
The paper tackles the problem of predicting outcomes for novel action-context pairs in causal imputation tasks, such as drug effects on different cell types, by framing it as matrix completion. The authors introduce a novel SCM-based model that induces a latent factor structure and show their method outperforms other matrix completion approaches on the PRISM drug repurposing dataset.
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.