Robust matrix completion from quantized observations

Jie Shen, Pranjal Awasthi, Ping Li

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations

Abstract

1-bit matrix completion refers to the problem of recovering a real-valued low-rank matrix from a small fraction of its sign patterns. In many real-world applications, however, the observations are not only highly quantized, but also grossly corrupted. In this work, we consider the noisy statistical model where each observed entry can be flipped with some probability after quantization. We propose a simple maximum likelihood estimator which is shown to be robust to the sign flipping noise. In particular, we prove an upper bound on the statistical error, showing that with overwhelming probability n = O (poly(1 − 2 E[τ])−2rd log d) samples are sufficient for accurate recovery, where r and d are the rank and dimension of the underlying matrix respectively, and τ ∈ [0, 1/2) is a random variable that parameterizes the sign flipping noise. Furthermore, a lower bound is established showing that the obtained sample complexity is near-optimal for prevalent statistical models. Finally, we substantiate our theoretical findings with a comprehensive study on synthetic and realistic data sets, and demonstrate the state-of-the-art performance.

Original languageEnglish (US)
StatePublished - 2020
Externally publishedYes
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: Apr 16 2019Apr 18 2019

Conference

Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
Country/TerritoryJapan
CityNaha
Period4/16/194/18/19

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Statistics and Probability

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