@inproceedings{80be6fc888674d92bc0c2049317567a9,
title = "A Minimax Lower Bound for Low-Rank Matrix-Variate Logistic Regression",
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.",
keywords = "logistic regression, low-rank matrix, minimax risk, singular value decomposition",
author = "Batoul Taki and Mohsen Ghassemi and Sarwate, {Anand D.} and Bajwa, {Waheed U.}",
note = "Funding Information: This work was supported by the US NSF Grants CCF-1910110 and CCF-1453073. Publisher Copyright: {\textcopyright} 2021 IEEE.; 55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021 ; Conference date: 31-10-2021 Through 03-11-2021",
year = "2021",
doi = "10.1109/IEEECONF53345.2021.9723149",
language = "English (US)",
series = "Conference Record - Asilomar Conference on Signals, Systems and Computers",
publisher = "IEEE Computer Society",
pages = "477--484",
editor = "Matthews, {Michael B.}",
booktitle = "55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021",
address = "United States",
}