LR-GLM: High-dimensional Bayesian inference using low-rank data approximations
Name
1905.07499.pdf
Description
Accepted version
Size
2.73 MB
Format
Adobe PDF
Checksum (MD5)
2112c870c55649fb2583bb6736cd2fdc
Author(s)
Trippe, Brian L.
Agrawal, Raj
Broderick, Tamara A
Date Issued
May 2019
Journal
Proceedings of the 36th International Conference on Machine Learning
Publisher
MIT Press
Citation
Trippe, Brian L. et al. “LR-GLM: High-dimensional Bayesian inference using low-rank data approximations.” Proceedings of the 36th International Conference on Machine Learning, 97 (May 2019): 6315-6324 © 2019 The Author(s)
Version
Author's final manuscript
Abstract
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework for such an analysis. In these high-dimensional problems, the number of covariates is often large relative to the number of observations, so we face non-trivial inferential uncertainty; a Bayesian approach allows coherent quantification of this uncertainty. Unfortunately, existing methods for Bayesian inference in GLMs require running times roughly cubic in parameter dimension, and so are limited to settings with at most tens of thousand parameters. We propose to reduce time and memory costs with a low-rank approximation of the data in an approach we call LR-GLM. When used with the Laplace approximation or Markov chain Monte Carlo, LR-GLM provides a full Bayesian posterior approximation and admits running times reduced by a full factor of the parameter dimension. We rigorously establish the quality of our approximation and show how the choice of rank allows a tunable computational-statistical trade-off. Experiments support our theory and demonstrate the efficacy of LR-GLM on real large-scale datasets.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://proceedings.mlr.press/v97/trippe19a.html
