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Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width
Christopher M De Sa · Ce Zhang · Kunle Olukotun · Christopher Ré

Tue Dec 08 04:00 PM -- 08:59 PM (PST) @ 210 C #47 #None

Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width. We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates, which have bounded hierarchy width—regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers.

Author Information

Christopher M De Sa (Stanford)
Ce Zhang (Wisconsin)
Kunle Olukotun (Stanford)

Kunle Olukotun is the Cadence Design Professor of Electrical Engineering and Computer Science at Stanford University. Olukotun is well known as a pioneer in multicore processor design and the leader of the Stanford Hydra chip multipocessor (CMP) research project. Olukotun founded Afara Websystems to develop high-throughput, low-power multicore processors for server systems. The Afara multicore processor, called Niagara, was acquired by Sun Microsystems. Niagara derived processors now power all Oracle SPARC-based servers. Olukotun currently directs the Stanford Pervasive Parallelism Lab (PPL), which seeks to proliferate the use of heterogeneous parallelism in all application areas using Domain Specific Languages (DSLs). Olukotun is a member of the Data Analytics for What’s Next (DAWN) Lab which is developing infrastructure for usable machine learning. Olukotun is an ACM Fellow and IEEE Fellow for contributions to multiprocessors on a chip and multi-threaded processor design and is the recipient of of the 2018 IEEE Harry H. Goode Memorial Award. Olukotun received his Ph.D. in Computer Engineering from The University of Michigan.

Chris Ré (Stanford)

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