[2312.10618] Sparse Learning and Class Probability Estimation with Weighted Support Vector Machines

Statistics > Methodology arXiv:2312.10618 (stat) [Submitted on 17 Dec 2023 (v1), last revised 24 Mar 2026 (this version, v2)] Title:Sparse Learning and Class Probability Estimation with Weighted Support Vector Machines Authors:Liyun Zeng, Hao Helen Zhang View a PDF of the paper titled Sparse Learning and Class Probability Estimation with Weighted Support Vector Machines, by Liyun Zeng and Hao Helen Zhang View PDF Abstract:Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of weighted Support Vector Machines (wSVMs) has demonstrated considerable promise in robustly and accurately predicting class probabilities and performing classification across a variety of problems (Wang et al., 2008). However, the existing framework relies on an $\ell^2$-norm regularized binary wSVMs optimization formulation, which is designed for dense features and exhibits limited performance in the presence of sparse features with redundant noise. Effective sparse learning thus requires prescreening of important variables for each binary wSVM to ensure accurate estimation of pairwise conditional probabilities. In this paper, we propose a novel class of wSVMs frameworks that incorporate automatic variable selection with accurate probability estimation for sparse learning problems. We developed efficient algorithms for var...