Recovering Latent Confounders from High-dimensional Proxy Variables
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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.
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References · 12
- 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
- 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 138
- 2020An Introduction to Proximal Causal Learningcited by 91
- 2020Semiparametric proximal causal inferencecited by 58
- 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
- 2019Robust Learning with the Hilbert-Schmidt Independence Criterioncited by 36
- 2022Learning Disentangled Representations for Counterfactual Regression via Mutual Information Minimizationcited by 18
- 2022Deep Multi-Modal Structural Equations For Causal Effect Estimation With Unstructured Proxiescited by 13
- 2013Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methodscited by 8
- 2017Matching Using Sufficient Dimension Reduction for Causal Inferencecited by 8
- 2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
- 2020Sufficient Dimension Reduction for Average Causal Effect Estimationcited by 6
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