Recovering Latent Confounders from High-dimensional Proxy Variables
Nathan Mankovich Homer Durand Emiliano Diaz Gherardo Varando Gustau Camps-Valls
Detecting latent confounders from proxy variables is an essential problem in
causal effect estimation. Previous approaches are limited to low-dimensional
proxies, sorted proxies, and binary treatments. We remove these assumptions and
present a novel Proxy Confounder Factorization (PCF) framework for continuous
treatment effect estimation when latent confounders manifest through
high-dimensional, mixed proxy variables. For specific sample sizes, our
two-step PCF implementation, using Independent Component Analysis (ICA-PCF),
and the end-to-end implementation, using Gradient Descent (GD-PCF), achieve
high correlation with the latent confounder and low absolute error in causal
effect estimation with synthetic datasets in the high sample size regime. Even
when faced with climate data, ICA-PCF recovers four components that explain
$75.9\%$ of the variance in the North Atlantic Oscillation, a known confounder
of precipitation patterns in Europe. Code for our PCF implementations and
experiments can be found here: https://github.com/IPL-UV/confound_it. The
proposed methodology constitutes a stepping stone towards discovering latent
confounders and can be applied to many problems in disciplines dealing with
high-dimensional observed proxies, e.g., spatiotemporal fields.