Minimax Bounds for Generalized Linear Models

Authors: Kuan-Yun Lee, Thomas Courtade

NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We establish a new class of minimax prediction error bounds for generalized linear models. Our bounds significantly improve previous results when the design matrix is poorly structured, including natural cases where the matrix is wide or does not have full column rank. Apart from the typical L2 risks, we study a class of entropic risks which recovers the usual L2 prediction and estimation risks, and demonstrate that a tight analysis of Fisher information can uncover underlying structural dependency in terms of the spectrum of the design matrix. The minimax approach we take differs from the traditional metric entropy approach, and can be applied to many other settings.
Researcher Affiliation Academia Kuan-Yun Lee and Thomas A. Courtade Department of Electrical Engineering and Computer Sciences University of California, Berkeley {timkylee,courtade}@berkeley.edu
Pseudocode No The paper is theoretical and does not contain any structured pseudocode or algorithm blocks.
Open Source Code No The paper is theoretical and does not provide any statement or link regarding concrete access to source code for the described methodology.
Open Datasets No The paper is theoretical and does not describe experimental evaluation on datasets, so no dataset availability information for training is provided.
Dataset Splits No The paper is theoretical and does not describe experimental evaluation on datasets, so no specific dataset split information for validation is provided.
Hardware Specification No The paper is theoretical and does not describe any experiments; therefore, no specific hardware details are provided.
Software Dependencies No The paper is theoretical and does not describe any experiments; therefore, no specific ancillary software details with version numbers are provided.
Experiment Setup No The paper is theoretical and does not describe any experiments or their setup, thus no specific experimental setup details are provided.