A Minimax Lower Bound for Low-Rank Matrix-Variate Logistic Regression

Batoul Taki, Mohsen Ghassemi, Anand D. Sarwate, Waheed U. Bajwa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers the problem of matrix-variate logistic regression. This paper derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by deriving a lower bound on the minimax risk. The bound depends explicitly on the dimension and distribution of the covariates, the rank and energy of the coefficient matrix, and the number of samples. The resulting bound is proportional to the intrinsic degrees of freedom in the problem, which suggests the sample complexity of the low-rank matrix logistic regression problem can be lower than that for vectorized logistic regression. The proof techniques utilized in this work also set the stage for development of minimax lower bounds for tensor-variate logistic regression problems.

Original languageEnglish (US)
Title of host publication55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages477-484
Number of pages8
ISBN (Electronic)9781665458283
DOIs
StatePublished - 2021
Externally publishedYes
Event55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021 - Virtual, Pacific Grove, United States
Duration: Oct 31 2021Nov 3 2021

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2021-October
ISSN (Print)1058-6393

Conference

Conference55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
Country/TerritoryUnited States
CityVirtual, Pacific Grove
Period10/31/2111/3/21

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

Keywords

  • logistic regression
  • low-rank matrix
  • minimax risk
  • singular value decomposition

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