Related papers: New Understanding of the Bethe Approximation and t…
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.,…
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…
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…
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…
The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an…
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…
We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi's Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a…
A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
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…
Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper,…
Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
We define and study an inference algorithm based on "belief propagation" (BP) and the Bethe approximation. The idea is to encode into a graph an a priori information composed of correlations or marginal probabilities of variables, and to…
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 fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles.…
When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy $F$, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An algorithm was recently…
Belief Propagation (BP) is one of the most popular methods for inference in probabilistic graphical models. BP is guaranteed to return the correct answer for tree structures, but can be incorrect or non-convergent for loopy graphical…
The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-field approximations, but which one performs better in the…
Scene graph generation aims to interpret an input image by explicitly modelling the potential objects and their relationships, which is predominantly solved by the message passing neural network models in previous methods. Currently, such…