DecoR: Deconfounding Time Series with Robust Regression

TL;DR

DecoR is a novel method for causal inference in time series data that effectively handles unobserved confounders by leveraging robust regression in the frequency domain, demonstrating accuracy and robustness in experiments.

Contribution

This work introduces DecoR, a new approach that frames deconfounding as an adversarial outlier problem in the frequency domain, with improved error bounds and no distributional assumptions.

Findings

DecoR achieves consistent causal effect estimation under spectral sparsity assumptions.

DecoR outperforms existing methods on synthetic and real-world Earth science data.

The approach is robust to model misspecification.

Abstract

Causal inference on time series data is a challenging problem, especially in the presence of unobserved confounders. This work focuses on estimating the causal effect between two time series that are confounded by a third, unobserved time series. Assuming spectral sparsity of the confounder, we show how in the frequency domain this problem can be framed as an adversarial outlier problem. We introduce Deconfounding by Robust regression (DecoR), a novel approach that estimates the causal effect using robust linear regression in the frequency domain. Considering two different robust regression techniques, we first improve existing bounds on the estimation error for such techniques. Crucially, our results do not require distributional assumptions on the covariates. We can therefore use them in time series settings. 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.