报告题目：Quantile Matrix Factorization: an Optimal Algorithm via Smooth Minimization

报告人: 刘鹏（英国肯特大学）

报告时间：2022年6月13日15:30-17:00

报告地点：腾讯会议ID:439 202 162

摘要：Matrix factorization is a critical technique in many applications. Most existing matrix factorization methods minimize the L2 loss between observations and their dependent matrix measurement variables. Under certain conditions, linear convergence to global optimality can be established for L2 loss, while L1 loss and check loss are widely used to deal with data that are contaminated with outliers, there lacks efficient and theoretically proved algorithms specifically designed for matrix factorization with non-smooth losses. In this paper, we study Quantile Matrix Factorization (QMF) that adopts a tuneable check loss and can introduce robustness to matrix estimation under possibly skewed and heavy-tailed observations, which are prevalent in reality. To deal with the non-smooth loss, we propose Nesterov-smoothed QMF (NsQMF), extending Nesterov’s optimal smooth approximation technique to matrix factorization. We then present an alternating minimization algorithm to solve NsQMF efficiently while handling the non-convexity. We prove that solving the smoothed NsQMF is equivalent to solving the original non-smooth QMF problem and that our algorithm achieves linear convergence to global optimality of QMF. Extensive evaluations verify our theoretical findings and demonstrate that NsQMF significantly outperforms commonly used Least Squares Matrix Factorization (LSMF) and prior rough smoothing techniques for QMF under various noise distributions.

报告人简介：

         刘鹏，英国肯特大学数学、统计与精算科学学院助理教授（tenured），英国高等教育学院会士（Fellow of the Higher Education Academy），美国《数学评论》(Mathematical Reviews)评论员。2010年获得华中师范大学数学与应用数学专业学士学位，2015年获得中国科学院数学与系统科学研究院统计学博士学位，曾先后在香港浸会大学数学系，美国华盛顿大学生物统计系，美国Fred Hutchinson Cancer Research Center，加拿大阿尔伯塔大学数学与统计系等科研院所工作。研究方向包括机器学习，强化学习，联邦学习，神经影像数据分析，生物统计，数据桥接。获得2018年国际数理统计学会IMS New Researcher Conference Travel Award。刘鹏博士在人工智能顶级会议AAAI, 数据挖掘顶级会议ICDM和机器学习顶级会议NeurIPS workshop等会议发表论文4篇，在国内外统计核心杂志发表论文6篇。主要参与Data Science with R, Deep Learning with Python, Statistics for Insurance等统计、精算专业本科和研究生课程的授课与课程设计，获得2022年肯特大学Above and Beyond Awards (Teaching)。