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The pairwise influence matrix of Dobrushin has long been used as an analytical tool to bound the rate of convergence of Gibbs sampling. In this work, we use Dobrushin influence as the basis of a practical tool to certify and efficiently improve the quality of a Gibbs sampler. Our Dobrushin-optimized Gibbs samplers (DoGS) offer customized variable selection orders for a given sampling budget and variable subset of interest, explicit bounds on total variation distance to stationarity, and certifiable improvements over the standard systematic and uniform random scan Gibbs samplers. In our experiments with image segmentation, Markov chain Monte Carlo maximum likelihood estimation, and Ising model inference, DoGS consistently deliver higher-quality inferences with significantly smaller sampling budgets than standard Gibbs samplers.
Summary/Notes]
Author Information
Ioannis Mitliagkas (Stanford University)
Ioannis Mitliagkas is a Postdoctoral Scholar with the departments of Statistics and Computer Science at Stanford University. He obtained his Ph.D. from the department of Electrical and Computer Engineering at The University of Texas at Austin. His research focuses on understanding and optimizing the scan order for Gibbs sampling, as well as understanding the interaction between optimization and the dynamics of large-scale learning systems. In the past he has worked on high-dimensional streaming problems and fast algorithms and computation for large graph problems.
Lester Mackey (Microsoft Research)
Lester Mackey is a machine learning researcher at Microsoft Research, where he develops new tools, models, and theory for large-scale learning tasks driven by applications from healthcare, climate, recommender systems, and the social good. Lester moved to Microsoft from Stanford University, where he was an assistant professor of Statistics and (by courtesy) of Computer Science. He earned his PhD in Computer Science and MA in Statistics from UC Berkeley and his BSE in Computer Science from Princeton University. He co-organized the second place team in the \$1M. Netflix Prize competition for collaborative filtering, won the \$50K Prise4Life ALS disease progression prediction challenge, won prizes for temperature and precipitation forecasting in the yearlong real-time \$800K Subseasonal Climate Forecast Rodeo, and received a best student paper award at the International Conference on Machine Learning.
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2017 Talk: Improving Gibbs Sampler Scan Quality with DoGS »
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