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

Tue Jun 11 11:35 AM -- 11:40 AM (PDT) @ Room 101

Due to the ease of modern data collection, practitioners often face a large collection of covariates and the need to understand their relation to some response. Generalized linear models (GLMs) offer a particularly interpretable framework for this analysis. In the high-dimensional case without an overwhelming amount of data per parameter, we expect uncertainty to be non-trivial; 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, thus limiting their applicability in increasingly widespread settings with tens of thousands of parameters. We propose to reduce time and memory costs with a low-rank approximation of the data. We show that our method, which we call LR-GLM, still provides a full Bayesian posterior approximation and admits running time reduced by a full factor of the parameter dimension. We theoretically establish the quality of our approximation via interpretable error bounds 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 in on real, large-scale datasets.

Author Information

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

Tamara Broderick is an Associate Professor in the Department of Electrical Engineering and Computer Science at MIT. She is a member of the MIT Laboratory for Information and Decision Systems (LIDS), 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. She has been awarded selection to the COPSS Leadership Academy (2021), an Early Career Grant (ECG) from the Office of Naval Research (2020), an AISTATS Notable Paper Award (2019), an NSF CAREER Award (2018), a Sloan Research Fellowship (2018), an Army Research Office Young Investigator Program (YIP) award (2017), Google Faculty Research Awards, an Amazon 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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