Topics in sparse Bayesian machine learning

Abstract

2023This dissertation is devoted to addressing several challenging problems in machine learning via the Bayesian approach. These problems frequently arise in diverse fields, such as epidemiology, biomedicine, robust statistics and imaging science, and are usually high-dimensional and have certain sparsity assumptions. In this dissertation, we will focus on three important problems, which are sparse canonical correlation analysis, minimum distance estimation and inverse problems. For each problem, we will develop a new method from the Bayesian perspective to solve it effectively and efficiently, with statistical guarantees and numerical evidence