DecoR: Deconfounding Time Series with Robust Regression
This addresses causal inference challenges in fields like Earth system science, offering a robust method for deconfounding time series data, though it is incremental as it builds on existing robust regression techniques.
The paper tackles the problem of estimating causal effects between time series in the presence of unobserved confounders by proposing DecoR, a method using robust regression in the frequency domain, and demonstrates its effectiveness with experiments on synthetic and real-world data, showing consistency and robustness to model misspecification.
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.