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Activity Number: 659 - Recent Advances in Dimension Reduction and Clustering
Type: Contributed
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #304704
Title: Matrix Completion Under Low-Rank Missing Mechanism
Author(s): Xiaojun Mao* and Raymond Wong and Song Xi Chen
Companies: Fudan University and Texas A&M University and Peking University
Keywords: Low-rank; Missing; Nuclear-norm; Regularization

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study matrix completion from corrupted data under a novel low-rank missing mechanism. The probability matrix of observation is estimated via a high dimensional low-rank matrix estimation procedure, and further used to complete the target matrix via inverse probabilities weighting. Due to both high dimensional and extreme (i.e., very small) nature of the true probability matrix, the effect of inverse probability weighting requires careful study. We derive optimal asymptotic convergence rates of the proposed estimators for both the observation probabilities and the target matrix.

Authors who are presenting talks have a * after their name.

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