Related papers: Loop series expansion with propagation diagrams

The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. Chertkov and Chernyak derived an interesting formula called Loop…

The Bethe approximation is a well-known approximation of the partition function used in statistical physics. Recently, an equality relating the partition function and its Bethe approximation was obtained for graphical models with binary…

A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the…

In this thesis, new generalizations of the Bethe approximation and new understanding of the replica method are proposed. The Bethe approximation is an efficient approximation for graphical models, which gives an asymptotically accurate…

We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including…

Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise…

The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g.,…

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006b) allows to express the exact partition function Z of a graphical model as a…

Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference,…

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…

Many quantities of interest in communications, signal processing, artificial intelligence, and other areas can be expressed as the partition sum of some factor graph. Although the exact calculation of the partition sum is in many cases…

Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…

Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion…

This paper resolves a common complexity issue in the Bethe approximation of statistical physics and the Belief Propagation (BP) algorithm of artificial intelligence. The Bethe approximation and the BP algorithm are heuristic methods for…

Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general.…

Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (Belief Propagation)-BP…

Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the Belief Propagation solution. By adding correction terms…

We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of [1, 2] is used to evaluate the resulting series expansion for the partition function. We show that, for…

In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum…

Probabilistic graphical models with frustration exhibit rugged energy landscapes that trap iterative optimization dynamics. These landscapes are shaped not only by local interactions, but crucially also by the global loop structure of the…