Optimization with Low-Rank Regularization

The Hong Kong University of Science and Technology
Department of Computer Science and Engineering

PhD Thesis Defence

Title: "Optimization with Low-Rank Regularization"


Mr. Quanming YAO


Low-rank modeling is important for machine learning, which has been widely 
used in many areas such as recommender systems and social network analysis 
in data mining, image and video processing in computer vision. 
Traditionally two approaches as factorization approach and nuclear norm 
regularization, are popularly used for low-rank matrix learning. In this 
thesis, we first propose an efficient algorithm based on proximal gradient 
descent for learning nuclear norm regularized problem, and a greedy 
algorithm to learn factorization approach which can deal with convex but 
possibly nonsmooth loss function. However, as larger singular values are 
more informative thus should be less penalized, low-rank matrix learning 
problem with adaptive nonconvex regularization is recently proposed, which 
also show better empirical performance. As existing algorithms can only 
solve small-scale problems, we develop a new algorithm, which is further 
accelerated and parallelized, scaling up the learning problem to large 
matrices. Finally, inspired by recent developments in proximal gradient 
descent for nonconvex optimization,

we propose a general and powerful problem transformation method which 
transfers a large family of nonconvex regularization problems back into 
convex ones. Such transformation can help reuse existing algorithms, which 
are originally designed for convex regularizers, now on nonconvex ones. As 
a result, the new algorithms can run much faster than the state-of-the-art 
on the original problems.

Date:			Thursday, 18 January 2018

Time:			2:00pm - 4:00pm

Venue:			Room 5501
 			Lifts 25/26

Chairman:		Prof. Rong Zheng (ISOM)

Committee Members:	Prof. James Kwok (Supervisor)
 			Prof. Lei Chen
 			Prof. Brian Mak
 			Prof. Jianfeng Cai (MATH)
 			Prof. Zhouchen Lin (Elec Engg & Comp Sci,
 					    Peking U)

**** ALL are Welcome ****