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科学研究
RESEARCH
Median Matrix Completion: from Embarrassment to Optimality
时间  Datetime
2019-07-21 14:00 — 15:00
地点  Venue
Zoom APP(2)()
报告人  Speaker
毛晓军
单位  Affiliation
复旦大学大数据学院
邀请人  Host
刘卫东
备注  remarks
Zoom会议号:648 016 53521 会议密码: 693228
报告摘要  Abstract

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge for large-scale data sets which are increasingly common among matrix completion problems. A simple solution to large-scale problems is parallel computing. However, embarrassingly parallel fashion often leads to inefficient estimators. Based on the idea of pseudo data, we propose a novel refinement step, which turns such inefficient estimators into a rate (near-)optimal matrix completion procedure. The refined estimator is an approximation of a regularized least median estimator, and therefore not an ordinary regularized empirical risk estimator. This leads to a non-standard analysis of asymptotic behaviors. Empirical results are also provided to confirm the effectiveness of the proposed method.