题  目：Optimal Smooth Approximation for Quantile Matrix Factorization

报告人：刘鹏 助理教授

时  间：2019年7月4日（星期四）下午3:00-4:00

地  点：财经校区教学楼八楼国际学术交流厅

报告摘要:

Matrix estimation and factorization have wide applications in signal processing and recommender systems. Most existing matrix factorization methods adopt a squared loss function and aim to recover a low-rank matrix to interpret conditional means of matrix entries given noisy observations. Quantile matrix factorization (QMF) adopts a check loss in matrix factorization and can better explain the central tendency of data under realistic noise distributions such as skewed and heavy-tailed noise. However, unlike Least Squares Matrix Factorization (LSMF), the non-smoothness of the check loss has posed significant computational challenges to QMF.

In this paper, we propose NsQMF, a nearly optimal smooth approximation procedure for QMF by extending Nesterov's optimal smooth approximation technique to nonconvex matrix factorization problems. We theoretically show that solving the nonsmooth QMF problem is equivalently to solving the proposed smooth approximation. We then present an efficient algorithm to solve QMF by adapting alternating minimization and a singular value projection algorithm to the proposed NsQMF. Extensive evaluations based on both synthetic and real-world data verify that NsQMF retains the exact recovery property and linear convergence rate of LSMF under the noiseless case and that NsQMF greatly outperforms LSMF and other prior smoothing techniques for QMF in terms of relative recover loss under a range of different noise distributions.

报告人简介：

刘鹏，英国肯特大学统计系助理教授（终身职位），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 Hutchnison癌症研究中心，加拿大阿尔伯塔大学数学与统计系工作。研究兴趣包括大数据，机器学习，加强学习，深度学习，函数型数据分析，生物统计。曾获得2018年国际数理统计学会IMS new researchers conference travel reward。已在《Statistica Sinica》、《Science in China：Mathematics》、《Annals of Institute of Statistical Mathematics》等主流统计杂志正式发表多篇高水平论文。

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2019年7月1日