# Doubly robust and computationally efficient high-dimensional variable selection

arXiv: https://arxiv.org/abs/2409.09512 · HTML: https://mlsanity.com/paper/2409.09512/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [General Frameworks for Conditional Two-Sample Testing](https://mlsanity.com/paper/2410.16636/) (2024)

## Abstract (arXiv)

Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure (PCM) test. However, directly deploying PCM for variable selection brings computational challenges: testing a single variable involves a few machine learning fits, so testing p variables requires O(p) fits. Inspired by model-X ideas, we observe that an estimate of the joint predictor distribution and a single response-on-all-predictors fit can be used to reconstruct all PCM fits. This yields tower PCM (tPCM), a computationally efficient extension of PCM to variable selection. When the joint predictor distribution is sufficiently tractable, as in applications like genome-wide association studies, tPCM offers a substantial speedup over PCM -- up to 130× in our simulations -- while matching its power. tPCM also improves on model-X methods like knockoffs and holdout randomization test (HRT) by returning per-variable p-values and improving speed, respectively. We prove that tPCM is doubly robust and asymptotically equivalent to both PCM and HRT. We thus extend the bridge between model-X and doubly robust approaches, demonstrating their independent arrival at equivalent methods and showing that this intersection is a fruitful source of new methodologies like tPCM.