Posterior contraction in group sparse logit models for categorical responses

TL;DR

This paper establishes posterior contraction rates for group sparse multi-category logit models, including multinomial cases, advancing Bayesian variable selection theory without size restrictions on true signals.

Contribution

It provides the first contraction results for multi-category group sparse logit models and refines Bayesian theory for binary logistic regression.

Findings

First-ever contraction properties for multi-category models

Unified framework for group sparsity in logit models

Refined Bayesian results for binary logistic regression

Abstract

This paper studies posterior contraction rates in multi-category logit models with priors incorporating group sparse structures. We consider a general class of logit models that includes the well-known multinomial logit models as a special case. Group sparsity is useful when predictor variables are naturally clustered and particularly useful for variable selection in the multinomial logit models. We provide a unified platform for posterior contraction rates of group-sparse logit models that include binary logistic regression under individual sparsity. No size restriction is directly imposed on the true signal in this study. In addition to establishing the first-ever contraction properties for multi-category logit models under group sparsity, this work also refines recent findings on the Bayesian theory of binary logistic regression.