Linglong Kong

University of Alberta

“Optimal Smooth Approximation for Quantile Matrix Factorization”

Date: Thursday, November 1, 2018

Matrix factorization has wide applications in recommender systems and signal processing. Existing matrix factorization methods are mostly based on squared loss and aim to yield a low-rank matrix to interpret conditional sample means. However, in many real applications with extreme data, least squares cannot explain their central tendency or tail distributions, incurring undesired estimates. In this paper, we study quantile matrix factorization (QMF), which introduces the check loss originated from quantile regression into matrix factorization. However, the non-smoothness of the check loss has brought significant challenges to numerical computation. We propose a nearly optimal and efficient algorithm to solve QMF by extending Nesterov's optimal smooth approximation procedure to the case of matrix factorization. We theoretically show that under certain conditions, the optimal solution to the proposed smooth approximation will converge to the optimal solution to the original nonsmooth and nonconvex QMF problem, with competitive convergence rates. Extensive simulations based on synthetic and real-world data have been conducted to verify our theoretical findings as well as algorithm performance.

Important Date

February 18 – February 22: Reading Week (No classes)

Upcoming Exam

STAT 1000 Midterm
Monday, March 4 at 5:30 p.m.

Upcoming Seminars

Statistics seminar: Aleeza Gerstein: “Levelling up R for Statistical Research and Teaching (Vignettes from RStudio::Conf)” — Thursday, February 28 at 2:45 p.m., P230 Duff Roblin.

Statistics seminar: Jame Fu: “Distribution of number of Levels in [s]-specified random permutation: A finite Markov Chain Imbedding Approach” — Thursday, March 7 at 2:45 p.m., P230 Duff Roblin.

Statistics seminar: Alison Gibbs: “Teaching Statistics in a Data Science World” — Thursday, March 21 at 2:45 p.m., P230 Duff Roblin.

Where are they now?

Llwellyn Maria Armstrong, M.Sc (1992)

Julie Mojica, M.Sc. (2003)