报告题目：一类鲁棒的低秩半定矩阵学习方法

题目英文：Efficient Low-Rank Semidefinite Programming with Robust Loss Functions

主讲人：胡恩良教授（云南师范大学数学学院教授）

时间：2024年1月4日（周四） 14:30 p.m.

形式：卓远楼403会议室

主办单位：信息学院

主持人：信息学院赵成贵副院长

摘要： In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this talk, I will focus on improving the robustness of a large class of learning algorithms that can be formulated as low-rank semidefinite programming problems. Traditional formulations use the square loss, which is notorious for being sensitive to outliers. We propose to replace this with more robust noise models, including the  l ₁-loss and other nonconvex losses. However, the resultant optimization problem becomes difficult as the objective is no longer convex or smooth. To alleviate this problem, we design an efficient algorithm based on majorization-minimization. The crux is on constructing a good optimization surrogate, and we show that this surrogate can be efficiently obtained by the alternating direction method of multipliers (ADMM). By properly monitoring ADMM’s convergence, the proposed algorithm is empirically efficient and also theoretically guaranteed to converge to a critical point. Extensive experiments are performed on several machine learning applications using both synthetic and real-world data sets. Results show that the proposed algorithm is not only fast but also has better performance than the state-of-the-arts.

主讲人简介：

胡恩良，云南师范大学数学学院教授、硕士生导师；中国计算机学会会员、中国人工智能学会机器学习专委会通讯委员、IEEE会员。博士毕业于南京航空航天大学计算机应用技术专业，曾到香港科技大学做Research Assistant和Postdoctoral Fellow工作，主要研究方向：机器学习中的大规模优化计算理论及算法。已在CCF-A类国际会议International Conference on Machine Learning、International Joint Conference on Artificial Intelligence，和信息类核心期刊《IEEE Transactions on Pattern Analysis and Machine Intelligence 》、《IEEE Transactions on Neural Networks and Learning Systems》、《IEEE Transactions on Neural Networks》、《Pattern Recognition》和《中国科学: 信息科学》等上发表论文二十余篇；主持研究国家自然科学基金项目三项。