# A Conditional Randomization Test for Sparse Logistic Regression in High-Dimension

3 S2A - Signal, Statistique et Apprentissage
LTCI - Laboratoire Traitement et Communication de l'Information
5 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data
NEUROSPIN - Service NEUROSPIN, Inria Saclay - Ile de France
9 CELESTE - Statistique mathématique et apprentissage
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay
Abstract : Identifying the relevant variables for a classification model with correct confidence levels is a central but difficult task in high-dimension. Despite the core role of sparse logistic regression in statistics and machine learning, it still lacks a good solution for accurate inference in the regime where the number of features p is as large as or larger than the number of samples n. Here we tackle this problem by improving the Conditional Randomization Test (CRT). The original CRT algorithm shows promise as a way to output p-values while making few assumptions on the distribution of the test statistics. As it comes with a prohibitive computational cost even in mildly high-dimensional problems, faster solutions based on distillation have been proposed. Yet, they rely on unrealistic hypotheses and result in low-power solutions. To improve this, we propose CRT-logit, an algorithm that combines a variable-distillation step and a decorrelation step that takes into account the geometry of $\ell_1$-penalized logistic regression problem. We provide a theoretical analysis of this procedure, and demonstrate its effectiveness on simulations, along with experiments on large-scale brain-imaging and genomics datasets.
Document type :
Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03680792
Contributor : Binh T. Nguyen Connect in order to contact the contributor
Submitted on : Sunday, May 29, 2022 - 11:47:34 AM
Last modification on : Wednesday, June 1, 2022 - 3:33:29 AM

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large-crt-arxiv.pdf
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### Identifiers

• HAL Id : hal-03680792, version 1

### Citation

Binh T. Nguyen, Bertrand Thirion, Sylvain Arlot. A Conditional Randomization Test for Sparse Logistic Regression in High-Dimension. 2022. ⟨hal-03680792⟩

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