English
Related papers

Related papers: Approximating the Permanent with Fractional Belief…

200 papers

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

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…

Artificial Intelligence · Computer Science 2013-03-22 Jinwoo Shin

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

While loopy belief propagation (LBP) performs reasonably well for inference in some Gaussian graphical models with cycles, its performance is unsatisfactory for many others. In particular for some models LBP does not converge, and in…

Machine Learning · Statistics 2015-05-28 Ying Liu , Venkat Chandrasekaran , Animashree Anandkumar , Alan S. Willsky

We present a novel distributed Gauss-Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially…

Information Theory · Computer Science 2018-08-28 Mirsad Cosovic , Dejan Vukobratovic

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…

Disordered Systems and Neural Networks · Physics 2009-11-11 Yoshiyuki Kabashima

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the…

Machine Learning · Computer Science 2014-01-17 Botond Cseke , Tom Heskes

This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the…

Numerical Analysis · Mathematics 2017-07-14 S. Allouch , M. Lucchesi , O. P. Le Maître , K. A. Mustapha , O. M. Knio

Most algorithms for propagating evidence through belief networks have been exact and exhaustive: they produce an exact (point-valued) marginal probability for every node in the network. Often, however, an application will not need…

Artificial Intelligence · Computer Science 2013-02-28 Denise L. Draper , Steve Hanks

Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic process with long-ranged correlations, represents a widely applied, paradigmatic mathematical model of anomalous diffusion. We report the results of…

In graphical models, factor graphs, and more generally energy-based models, the interactions between variables are encoded by a graph, a hypergraph, or, in the most general case, a partially ordered set (poset). Inference on such…

Machine Learning · Statistics 2025-10-08 Grégoire Sergeant-Perthuis , Léo Boitel

Data association, the reasoning over correspondence between targets and measurements, is a problem of fundamental importance in target tracking. Recently, belief propagation (BP) has emerged as a promising method for estimating the marginal…

Artificial Intelligence · Computer Science 2018-01-25 Jason L. Williams , Roslyn A. Lau

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…

Physics and Society · Physics 2007-05-23 Cyril Furtlehner , Jean-Marc Lasgouttes , Arnaud De La Fortelle

The permanent of a non-negative matrix appears naturally in many information processing scenarios. Because of the intractability of the permanent beyond small matrices, various approximation techniques have been developed in the past. In…

Combinatorics · Mathematics 2022-05-31 Kit Shing Ng , Pascal O. Vontobel

Fractional Brownian motion (fBm) is an important scale-invariant Gaussian non-Markovian process with stationary increments, which serves as a prototypical example of a system with long-range temporal correlations and anomalous diffusion.…

Statistical Mechanics · Physics 2026-04-29 Baruch Meerson , Pavel V. Sasorov

Gaussian belief propagation (GaBP) is an iterative algorithm for computing the mean of a multivariate Gaussian distribution, or equivalently, the minimum of a multivariate positive definite quadratic function. Sufficient conditions, such as…

Information Theory · Computer Science 2014-01-07 Nicholas Ruozzi , Sekhar Tatikonda

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

Belief propagation is an algorithm that is known from statistical physics and computer science. It provides an efficient way of calculating marginals that involve large sums of products which are efficiently rearranged into nested products…

Artificial Intelligence · Computer Science 2020-12-22 Tim Ritmeester , Hildegard Meyer-Ortmanns

Due to the intractable nature of exact lifted inference, research has recently focused on the discovery of accurate and efficient approximate inference algorithms in Statistical Relational Models (SRMs), such as Lifted First-Order Belief…

Artificial Intelligence · Computer Science 2016-07-01 David Smith , Parag Singla , Vibhav Gogate

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