Poster
LR-GLM: High-Dimensional Bayesian Inference Using Low-Rank Data Approximations
Brian Trippe · Jonathan Huggins · Raj Agrawal · Tamara Broderick

Tue Jun 11th 06:30 -- 09:00 PM @ Pacific Ballroom #214

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.

Author Information

Brian Trippe (MIT)
Jonathan Huggins (Harvard)
Raj Agrawal (MIT)
Tamara Broderick (MIT)

Tamara Broderick is the ITT Career Development Assistant Professor in the Department of Electrical Engineering and Computer Science at MIT. She is a member of the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL), the MIT Statistics and Data Science Center, and the Institute for Data, Systems, and Society (IDSS). She completed her Ph.D. in Statistics at the University of California, Berkeley in 2014. Previously, she received an AB in Mathematics from Princeton University (2007), a Master of Advanced Study for completion of Part III of the Mathematical Tripos from the University of Cambridge (2008), an MPhil by research in Physics from the University of Cambridge (2009), and an MS in Computer Science from the University of California, Berkeley (2013). Her recent research has focused on developing and analyzing models for scalable Bayesian machine learning---especially Bayesian nonparametrics. She has been awarded an NSF CAREER Award (2018), a Sloan Research Fellowship (2018), an Army Research Office Young Investigator Program award (2017), a Google Faculty Research Award, the ISBA Lifetime Members Junior Researcher Award, the Savage Award (for an outstanding doctoral dissertation in Bayesian theory and methods), the Evelyn Fix Memorial Medal and Citation (for the Ph.D. student on the Berkeley campus showing the greatest promise in statistical research), the Berkeley Fellowship, an NSF Graduate Research Fellowship, a Marshall Scholarship, and the Phi Beta Kappa Prize (for the graduating Princeton senior with the highest academic average).

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