Year: 2024
Type: preprint
Abstract: This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the likelihood resulting the fractional posterior. Our study yields concentration results for the fractional posterior, not only on the joint distribution of the predictor and response variable but also for the regression coefficients. Significantly, we derive novel findings concerning misclassification excess risk bounds using sparse generalized Bayesian logistic regression. These results parallel recent findings for penalized methods in the frequentist literature. Furthermore, we extend our results to the scenario of model misspecification, which is of critical importance.
Source: arXiv (Cornell University)
Author: Mai, The Tien
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Norges Forskningsråd
Award: G7275849276
OpenAlex ID: W4393027653