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The k-tied Normal Distribution: A Compact Parameterization of Gaussian Mean Field Posteriors in Bayesian Neural Networks
Jakub Swiatkowski · Kevin Roth · Bastiaan Veeling · Linh Tran · Joshua V Dillon · Jasper Snoek · Stephan Mandt · Tim Salimans · Rodolphe Jenatton · Sebastian Nowozin

Thu Jul 16 12:00 PM -- 12:45 PM & Fri Jul 17 01:00 AM -- 01:45 AM (PDT) @ None #None

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. In contrast, here we share a curious experimental finding that suggests instead restricting the variational distribution to a more compact parameterization. For a variety of deep Bayesian neural networks trained using Gaussian mean-field variational inference, we find that the posterior standard deviations consistently exhibit strong low-rank structure after convergence. This means that by decomposing these variational parameters into a low-rank factorization, we can make our variational approximation more compact without decreasing the models' performance. Furthermore, we find that such factorized parameterizations improve the signal-to-noise ratio of stochastic gradient estimates of the variational lower bound, resulting in faster convergence.

Author Information

Jakub Swiatkowski (University of Warsaw)
Kevin Roth (ETH Zurich)
Bastiaan Veeling (University of Amsterdam)
Linh Tran (Imperial College London)
Josh V Dillon (Google)
Jasper Snoek (Google Brain)
Stephan Mandt (University of California, Irivine)

Stephan Mandt is an Assistant Professor of Computer Science at the University of California, Irvine. From 2016 until 2018, he was a Senior Researcher and head of the statistical machine learning group at Disney Research, first in Pittsburgh and later in Los Angeles. He held previous postdoctoral positions at Columbia University and at Princeton University. Stephan holds a PhD in Theoretical Physics from the University of Cologne. He is a Fellow of the German National Merit Foundation, a Kavli Fellow of the U.S. National Academy of Sciences, and was a visiting researcher at Google Brain. Stephan serves regularly as an Area Chair for NeurIPS, ICML, AAAI, and ICLR, and is a member of the Editorial Board of JMLR. His research is currently supported by NSF, DARPA, IBM, and Qualcomm.

Tim Salimans (Google)
Rodolphe Jenatton (Google Research)
Sebastian Nowozin (Microsoft Research)

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