DecoR: deconfounding time series with robust regression

• 成果类型: Article
• 署名作者: Schur, Felix; Blieske, Pio; Peters, Jonas
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkaf067
• 发表日期: 2026-07
• 页码: 799-818
• 关键词: Causal Inference; confounding; earth system science; robust regression; time series analysis; EQUATION MODELS; north-america; variability; ensemble

摘要

Causal inference on time series data is a challenging problem, especially in the presence of unobserved confounders. In this work, we focus on estimating the causal effect of a multivariate time series on a univariate time series when a third (possibly multivariate) time series confounds the relationship but remains unobserved. By assuming spectral sparsity of the confounder, we show how this problem can be framed as an adversarial outlier problem in the frequency domain. We introduce Deconfounding by Robust regression (DecoR), a novel approach that estimates the causal effect using robust linear regression in the frequency domain. We consider two robust regression techniques and provide improved bounds on their estimation errors. Applying these results to DecoR, we prove, under suitable assumptions, upper bounds for the estimation error of DecoR that imply consistency. We demonstrate DecoR's effectiveness through experiments on both synthetic and real-world data from Earth system science. The simulation experiments furthermore suggest that DecoR is robust with respect to model misspecification.