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Structured Stochastic Gradient MCMC
Antonios Alexos · Alex Boyd · Stephan Mandt

Wed Jul 20 03:30 PM -- 05:30 PM (PDT) @ Hall E #719

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is a scalable algorithm for asymptotically exact Bayesian inference in parameter-rich models, such as Bayesian neural networks. However, since mixing can be slow in high dimensions, practitioners often resort to variational inference (VI). Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. To relax these assumptions, this work proposes a new non-parametric variational inference scheme that combines ideas from both SGMCMC and coordinate-ascent VI. The approach relies on a new Langevin-type algorithm that operates on a "self-averaged" posterior energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies between coordinates can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SGMCMC and parametric VI.

Author Information

Antonios Alexos (University of California, Irvine)
Alex Boyd (University of California, Irvine)
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.

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