2009/01/07 by Vicenç Gómez, V. Gómez, Hilbert J. Kappen +6
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Error Correcting Code Techniques #FOS: Computer and information sciences #Machine Learning and Algorithms #cs.AI
paper · pdf · doi:10.48550/arxiv.0901.0786
23 pages, 10 figures. Submitted to Journal of Machine Learning Research. Proceedings version accepted for UAI 2009
openalex publication_date 2009/01/07 · arxiv created 2009/05/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006) allows to express the exact partition function of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in (Certkov et al., 2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze the performance of the algorithm for the partition function approximation for models with binary variables and pairwise interactions on grids and other planar graphs. We study in detail both the loop series and the equivalent Pfaffian series and show that the first term of the Pfaffian series for the general, intractable planar model, can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.