Continuous Markov random fields are a general formalism to model joint probability distributions over events with continuous outcomes. We prove that marginal computation for constrained continuous MRFs is #P-hard in general and present a polynomial-time approximation scheme under mild assumptions on the structure of the random field. Moreover, we introduce a sampling algorithm to compute marginal distributions and develop novel techniques to increase its efficiency. Continuous MRFs are a general purpose probabilistic modeling tool and we demonstrate how they can be applied to statistical relational learning. On the problem of collective classification, we evaluate our algorithm and show that the standard deviation of marginals serves as a useful measure of confidence.
Matthias Broecheler (University of Maryland CP)
Lise Getoor (UC Santa Cruz)
Lise Getoor is an Associate Professor in the Computer Science Department and the Institute for Advanced Computer Studies at the University of Maryland, College Park. Her research areas include machine learning, reasoning under uncertainty, and database management. She is co-editor with Ben Taskar of the book 'An Introduction to Statistical Relational Learning', MIT Press, 2007. She is a board member of the International Machine Learning Society, and has served as Machine Learning Journal Action Editor, Associate Editor for the ACM Transactions of Knowledge Discovery from Data, JAIR Associate Editor, and on the AAAI Council. She is a recipient of several best paper awards, an NSF Career Award and a National Physical Sciences Consortium Fellowship. She received her PhD from Stanford University, her Master’s degree from the University of California, Berkeley, and her undergraduate degree from the University of California, Santa Barbara.
More from the Same Authors
2012 Poster: Scaling MPE Inference for Constrained Continuous Markov Random Fields with Consensus Optimization »
Stephen H Bach · Matthias Broecheler · Lise Getoor · Dianne P O'Leary
2012 Tutorial: Representation, Inference and Learning in Structured Statistical Models »
2007 Workshop: Statistical Network Models »
Kevin P Murphy · Lise Getoor · Eric Xing · Raphael Gottardo