Yuta Hayashida | Searcharxiv

arXiv2026

Information Gap and Feasibility-Aware Inference in Binomial Logistic Mixtures

This paper studies the information gap between mixture detection and label recovery in binomial logistic mixtures. Standard likelihood-based criteria such as the Bayesian information criterion (BIC) can detect the presence of two components, but this does not guarantee that the corresponding labels are recoverable. We show that this gap is intrinsic to binomial logistic mixtures with a fixed number of trials: observed-data evidence for mixture structure and per-observation information for label recovery have different local orders in the component separation, and only the former accumulates with the sample size. As a result, there exists a detectable-but-unrecoverable regime in which BIC selects two components while the posterior labels remain essentially uninformative. To address this issue, we propose two feasibility-aware inference procedures: a recoverability-aware BIC with a posterior-entropy penalty and an entropy-regularized estimator that mitigates the tendency of the maximum likelihood estimator to produce overly separated components and overly concentrated posterior responsibilities. Numerical experiments confirm the predicted gap and demonstrate that the proposed methods avoid misleading component selections and improve the calibration of posterior label probabilities.

stat.ML↗

arXiv2025

Repulsive g-Priors for Regression Mixtures

Mixture regression models are powerful tools for capturing heterogeneous covariate-response relationships, yet classical finite mixtures and Bayesian nonparametric alternatives often suffer from instability or overestimation of clusters when component separability is weak. Recent repulsive priors improve parsimony in density mixtures by discouraging nearby components, but their direct extension to regression is nontrivial since separation must respect the predictive geometry induced by covariates. We propose a repulsive g-prior for regression mixtures that enforces separation in the Mahalanobis metric, penalizing components indistinguishable in the predictive mean space. This construction preserves conjugacy-like updates while introducing geometry-aware interactions, enabling efficient blocked-collapsed Gibbs sampling. Theoretically, we establish tractable normalizing bounds, posterior contraction rates, and shrinkage of tail mass on the number of components. Simulations under correlated and overlapping designs demonstrate improved clustering and prediction relative to independent, Euclidean-repulsive, and sparsity-inducing baselines.

stat.ME↗