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Pré-Publication, Document De Travail Année : 2023

SIGLE: a valid procedure for Selective Inference with the Generalized Linear Lasso

Résumé

This article investigates uncertainty quantification of the generalized linear lasso~(GLL), a popular variable selection method in high-dimensional regression settings. In many fields of study, researchers use data-driven methods to select a subset of variables that are most likely to be associated with a response variable. However, such variable selection methods can introduce bias and increase the likelihood of false positives, leading to incorrect conclusions. In this paper, we propose a post-selection inference framework that addresses these issues and allows for valid statistical inference after variable selection using GLL. We show that our method provides accurate $p$-values and confidence intervals, while maintaining high statistical power. In a second stage, we focus on the sparse logistic regression, a popular classifier in high-dimensional statistics. We show with extensive numerical simulations that SIGLE is more powerful than state-of-the-art PSI methods. SIGLE relies on a new method to sample states from the distribution of observations conditional on the selection event. This method is based on a simulated annealing strategy whose energy is given by the first order conditions of the logistic lasso.
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Dates et versions

hal-03622196 , version 1 (28-03-2022)
hal-03622196 , version 2 (31-07-2022)
hal-03622196 , version 3 (04-07-2023)

Identifiants

Citer

Quentin Duchemin, Yohann de Castro. SIGLE: a valid procedure for Selective Inference with the Generalized Linear Lasso. 2023. ⟨hal-03622196v3⟩
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