# Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding

arXiv: https://arxiv.org/abs/2004.03758 · HTML: https://mlsanity.com/paper/2004.03758/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 9 of 9)

- [Ice Cream Doesn't Cause Drowning: Benchmarking LLMs Against Statistical Pitfalls in Causal Inference](https://mlsanity.com/paper/2505.13770/) (2025)
- [Simultaneous inference for generalized linear models with unmeasured confounders](https://mlsanity.com/paper/2309.07261/) (2023)
- [Correcting Confounding via Random Selection of Background Variables](https://mlsanity.com/paper/2202.02150/) (2022)
- [Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning](https://mlsanity.com/paper/2407.13666/) (2024)
- [Substitute adjustment via recovery of latent variables](https://mlsanity.com/paper/2403.00202/) (2024)
- [ExMAG: Learning of Maximally Ancestral Graphs](https://mlsanity.com/paper/2503.08245/) (2025)
- [Double Machine Learning for Adaptive Causal Representation in High-Dimensional Data](https://mlsanity.com/paper/2411.14665/) (2024)
- [Deconfounded Warm-Start Thompson Sampling with Applications to Precision Medicine](https://mlsanity.com/paper/2505.17283/) (2025)
- [Spectrally Deconfounded Gradient Boosting](https://mlsanity.com/paper/2607.09371/) (2026)

## Abstract (arXiv)

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected by hidden confounding and propose the em Doubly Debiased Lasso estimator for individual components of the regression coefficient vector. Our advocated method simultaneously corrects both the bias due to estimation of high-dimensional parameters as well as the bias caused by the hidden confounding. We establish its asymptotic normality and also prove that it is efficient in the Gauss-Markov sense. The validity of our methodology relies on a dense confounding assumption, i.e. that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application.