# DecoR: Deconfounding Time Series with Robust Regression

arXiv: https://arxiv.org/abs/2406.07005 · HTML: https://mlsanity.com/paper/2406.07005/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Efficient Algorithms and Lower Bounds for Robust Linear Regression](https://mlsanity.com/paper/1806.00040/) (2018)
- [Efficient Algorithms for Outlier-Robust Regression](https://mlsanity.com/paper/1803.03241/) (2018)
- [Robust regression with covariate filtering: Heavy tails and adversarial contamination](https://mlsanity.com/paper/2009.12976/) (2020)
- [Robust Regression via Hard Thresholding](https://mlsanity.com/paper/1506.02428/) (2015)
- [Adaptive Hard Thresholding for Near-optimal Consistent Robust Regression](https://mlsanity.com/paper/1903.08192/) (2019)
- [Spectral Deconfounding via Perturbed Sparse Linear Models](https://mlsanity.com/paper/1811.05352/) (2018)
- [Consistent regression when oblivious outliers overwhelm](https://mlsanity.com/paper/2009.14774/) (2020)
- [Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Past](https://mlsanity.com/paper/2203.06056/) (2022)
- [Robust estimation with Lasso when outputs are adversarially contaminated](https://mlsanity.com/paper/2004.05990/) (2020)
- [Spatial+: a novel approach to spatial confounding](https://mlsanity.com/paper/2009.09420/) (2020)
- [Spectral Deconfounding for High-Dimensional Sparse Additive Models](https://mlsanity.com/paper/2312.02860/) (2023)
- [Selecting a Scale for Spatial Confounding Adjustment](https://mlsanity.com/paper/1909.11161/) (2019)
- [A spectral adjustment for spatial confounding](https://mlsanity.com/paper/2012.11767/) (2020)

## Built on by (most cited first, 2 of 2)

- [Structural Causal Bottleneck Models](https://mlsanity.com/paper/2603.08682/) (2026)
- [Using Time Structure to Estimate Causal Effects](https://mlsanity.com/paper/2504.11076/) (2025)

## Abstract (arXiv)

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.