Coupling Generative Modeling and an Autoencoder with the Causal Bridge

ruolin meng, Ming-Yu Chung, Dhanajit Brahma, Ricardo Henao, Lawrence Carin

Keywords: Causal Effect Estimation, Proxy Causal Learning, Causal Bridge

TL;DR: We present a new theoretical perspective for the causal bridge that allows a deeper understanding of the impact of its assumptions on causal estimates while yielding an autoencoder formulation that improves causal effect estimation.

Abstract: We consider inferring the causal effect of a treatment (intervention) on an outcome of interest in situations where there is potentially an unobserved confounder influencing both the treatment and the outcome. This is achievable by assuming access to two separate sets of control (proxy) measurements associated with treatment and outcomes, which are used to estimate treatment effects through a function termed the *causal bridge* (CB). We present a new theoretical perspective, associated assumptions for when estimating treatment effects with the CB is feasible, and a bound on the average error of the treatment effect when the CB assumptions are violated. From this new perspective, we then demonstrate how coupling the CB with an autoencoder architecture allows for the sharing of statistical strength between observed quantities (proxies, treatment, and outcomes), thus improving the quality of the CB estimates. Experiments on synthetic and real-world data demonstrate the effectiveness of the proposed approach relative to state-of-the-art methodology for causal inference with proxy measurements.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 13812