Speaker: 陈丙振博士，杭州电子科技大学

Inviter: 陈黄岳

Title: Convoluted Support Matrix Machine in High Dimensions

Language: Chinese

Time & Venue: 2024.06.12 15:30-16:30 腾讯会议：511-847-862

Abstract: The Support Vector Machine (SVM) has been successfully applied to various discrimination problems. Recently, there has been growing interest in expanding the traditional vector-based SVM to accommodate structured matrix inputs. However, the nonsmooth hinge loss presents significant challenges for both theoretical and computational development. We propose a convex smoothing procedure for the hinge loss to address these challenges. Additionally, we introduce an elastic-net type penalty to handle high-dimensional matrix inputs. We argue that the resulting approach is significantly more appealing than the standard SVM for discrimination with high-dimensional matrix inputs. Our proposed method yields an estimate with a provably optimal statistical convergence rate. Moreover, the smooth and convex loss function enables the development of a highly efficient optimization algorithm. Our optimization algorithm enjoys a fast linear convergence rate with a simple implementation. We substantiate the superiority of our proposal on classification accuracy and computational efficiency through comprehensive simulations and an application to an electroencephalograph dataset.