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arXiv · 2006.10400

Median Matrix Completion: from Embarrassment to Optimality

Weidong Liu·Xiaojun Mao·Raymond K. W. Wong
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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.

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Weidong Liu, Xiaojun Mao, Raymond K. W. Wong. 2020-06-18. Median Matrix Completion: from Embarrassment to Optimality. https://arxiv.org/abs/2006.10400

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