2012/10/19 by Tom Heskes, Heskes, Tom, Kees Albers +4
Computer Science · Mathematics · #Artificial Intelligence (cs.AI) #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #cs.AI #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1212.2480
Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003)
arxiv created 2012/10/19 · openalex publication_date 2012/10/19 · arxiv updated 2012/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy. However, belief propagation does not always converge, which explains the need for approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP and UPS. Here we describe a class of algorithms that solves this typically nonconvex constrained minimization of the Kikuchi free energy through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speed-ups over CCCP.