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Smoothed Gradients for Stochastic Variational Inference
Stephan Mandt · David Blei

Thu Dec 11 11:00 AM -- 03:00 PM (PST) @ Level 2, room 210D

Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-compute noisy natural gradients. As with most traditional stochastic optimization methods, SVI takes precautions to use unbiased stochastic gradients whose expectations are equal to the true gradients. In this paper, we explore the idea of following biased stochastic gradients in SVI. Our method replaces the natural gradient with a similarly constructed vector that uses a fixed-window moving average of some of its previous terms. We will demonstrate the many advantages of this technique. First, its computational cost is the same as for SVI and storage requirements only multiply by a constant factor. Second, it enjoys significant variance reduction over the unbiased estimates, smaller bias than averaged gradients, and leads to smaller mean-squared error against the full gradient. We test our method on latent Dirichlet allocation with three large corpora.

Author Information

Stephan Mandt (University of California, Irvine)
Stephan Mandt

Stephan Mandt is an Associate Professor of Computer Science and Statistics 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 in Pittsburgh and Los Angeles. He held previous postdoctoral positions at Columbia University and Princeton University. Stephan holds a Ph.D. in Theoretical Physics from the University of Cologne, where he received the German National Merit Scholarship. He is furthermore a recipient of the NSF CAREER Award, the UCI ICS Mid-Career Excellence in Research Award, the German Research Foundation's Mercator Fellowship, a Kavli Fellow of the U.S. National Academy of Sciences, a member of the ELLIS Society, and a former visiting researcher at Google Brain. Stephan regularly serves as an Area Chair, Action Editor, or Editorial Board member for NeurIPS, ICML, AAAI, ICLR, TMLR, and JMLR. His research is currently supported by NSF, DARPA, DOE, Disney, Intel, and Qualcomm.

David Blei (Columbia University)

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