# Recovering Latent Confounders from High-dimensional Proxy Variables

arXiv: https://arxiv.org/abs/2403.14228 · HTML: https://mlsanity.com/paper/2403.14228/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Robust Learning with the Hilbert-Schmidt Independence Criterion](https://mlsanity.com/paper/1910.00270/) (2019)
- [Learning Disentangled Representations for Counterfactual Regression via Mutual Information Minimization](https://mlsanity.com/paper/2206.01022/) (2022)
- [Deep Multi-Modal Structural Equations For Causal Effect Estimation With Unstructured Proxies](https://mlsanity.com/paper/2203.09672/) (2022)
- [Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods](https://mlsanity.com/paper/1310.5089/) (2013)
- [Matching Using Sufficient Dimension Reduction for Causal Inference](https://mlsanity.com/paper/1702.00444/) (2017)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Sufficient Dimension Reduction for Average Causal Effect Estimation](https://mlsanity.com/paper/2009.06444/) (2020)

## Abstract (arXiv)

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/confoundit. 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.