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Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually.…

Machine Learning · Statistics 2024-10-30 Christian Knoll , Adrian Weller , Franz Pernkopf

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…

Artificial Intelligence · Computer Science 2012-06-26 Alexander T. Ihler

Message passing type algorithms such as the so-called Belief Propagation algorithm have recently gained a lot of attention in the statistics, signal processing and machine learning communities as attractive algorithms for solving a variety…

Discrete Mathematics · Computer Science 2016-03-10 David Gamarnik , Devavrat Shah , Yehua Wei

Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has…

Data Structures and Algorithms · Computer Science 2012-11-15 Tobias Brunsch , Kamiel Cornelissen , Bodo Manthey , Heiko Röglin

We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP)…

Information Theory · Computer Science 2015-03-13 Mohsen Bayati , Christian Borgs , Jennifer Chayes , Riccardo Zecchina

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.…

Machine Learning · Computer Science 2019-05-27 Frederic Koehler

Belief Propagation (BP) is an important message-passing algorithm for various reasoning tasks over graphical models, including solving the Constraint Optimization Problems (COPs). It has been shown that BP can achieve state-of-the-art…

Artificial Intelligence · Computer Science 2022-09-27 Yanchen Deng , Shufeng Kong , Caihua Liu , Bo An

Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…

Statistics Theory · Mathematics 2018-12-27 Maxime Lenormand , Franck Jabot , Guillaume Deffuant

The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…

Information Theory · Computer Science 2012-12-18 Nima Noorshams , Martin J. Wainwright

Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of…

Data Structures and Algorithms · Computer Science 2015-09-24 Sungsoo Ahn , Sejun Park , Michael Chertkov , Jinwoo Shin

Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the…

Machine Learning · Statistics 2017-05-31 Christian Knoll , Franz Pernkopf , Dhagash Mehta , Tianran Chen

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…

Mathematical Physics · Physics 2008-12-25 Yusuke Watanabe , Kenji Fukumizu

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…

Machine Learning · Statistics 2025-02-06 Harald Leisenberger , Franz Pernkopf

We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued…

Statistical Mechanics · Physics 2009-11-11 T. Rizzo , B. Wemmenhove , H. J. Kappen

MAP is the problem of finding a most probable instantiation of a set of nvariables in a Bayesian network, given some evidence. MAP appears to be a significantly harder problem than the related problems of computing the probability of…

Artificial Intelligence · Computer Science 2013-01-07 James D. Park

A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…

Probability · Mathematics 2017-11-17 Victor Bapst , Amin Coja-Oghlan

How the brain performs credit assignment is a fundamental unsolved problem in neuroscience. Many `biologically plausible' algorithms have been proposed, which compute gradients that approximate those computed by backpropagation (BP), and…

Machine Learning · Computer Science 2022-08-05 Beren Millidge , Yuhang Song , Tommaso Salvatori , Thomas Lukasiewicz , Rafal Bogacz

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…

Machine Learning · Statistics 2020-01-29 Sungsoo Ahn , Michael Chertkov , Adrian Weller , Jinwoo Shin

This work describes a method of approximating matrix permanents efficiently using belief propagation. We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this…

Machine Learning · Computer Science 2009-08-13 Bert Huang , Tony Jebara

A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by…

Artificial Intelligence · Computer Science 2012-05-14 Kristian Kersting , Babak Ahmadi , Sriraam Natarajan