Work

Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior

Year: 2012

Type: conference-paper

Abstract: In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and expensive cross-validation to find the optimal regularization parameter. Moreover, the model's predictive performance may degrade dramatically with a suboptimal value of the regularization parameter (which is sometimes desirable to induce sparseness). We propose a fully Bayesian approach based on a "spike and slab" prior (similar to L0 regularization) that does not suffer from these shortcomings. We develop an approximate MCMC method combining Langevin dynamics and reversible jump MCMC to conduct inference in this model. Experiments show that the proposed model learns a good combination of the structure and parameter values without the need for separate hyper-parameter tuning. Moreover, the model's predictive performance is much more robust than L1-based methods with hyper-parameter settings that induce highly sparse model structures.

Source: UvA-DARE (University of Amsterdam)

DOI: 10.48550/arxiv.1206.1088

Authors: Chen, Yutian, Welling, Max

Institutions: University of California, Irvine, Irvine University

Language: English

Topic: Bayesian Modeling and Causal Inference

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: RI:Small:Collaborative Research: Infinite Bayesian Networks for Hierarchical Visual Categorization, PRISM: UCI Interdisciplinary computational and applied mathematics program, IIS: RI: Small: Nonlinear Dynamical System Theory for Machine Learning