Recovering Latent Confounders from High-dimensional Proxy Variables ...

• Main Authors: Mankovich, Nathan, Durand, Homer, Diaz, Emiliano, Varando, Gherardo, Camps-Valls, Gustau
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2024
• Subjects: Machine Learning stat.ML; Machine Learning cs.LG; FOS Computer and information sciences; North Atlantic; North Atlantic oscillation
• Online Access: https://dx.doi.org/10.48550/arxiv.2403.14228; https://arxiv.org/abs/2403.14228

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: ...