Bayesian Analysis for Over-parameterized Linear Model without Sparsity

arXiv:2305.15754v2 Announce Type: replace-cross
Abstract: In the field of high-dimensional Bayesian statistics, a plethora of methodologies have been developed, including various prior distributions that result in parameter sparsity. However, such priors exhibit limitations in handling the spectral eigenvector structure of data, rendering estimations less effective for analyzing the over-parameterized models (high-dimensional linear models that do not assume sparsity) developed in recent years. This study introduces a Bayesian approach that employs a prior distribution dependent on the eigenvectors of data covariance …

abstract analysis arxiv bayesian data estimations however limitations linear linear model math.st prior rendering sparsity statistics stat.me stat.ml stat.th type