Related papers: Belief Propagation Min-Sum Algorithm for Generaliz…
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)…
In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network…
The group testing problem asks for efficient pooling schemes and algorithms that allow to screen moderately large numbers of samples for rare infections. The goal is to accurately identify the infected samples while conducting the least…
We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the…
Variational inference algorithms such as belief propagation have had tremendous impact on our ability to learn and use graphical models, and give many insights for developing or understanding exact and approximate inference. However,…
An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute…
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…
We apply belief propagation (BP) to multi--user detection in a spread spectrum system, under the assumption of Gaussian symbols. We prove that BP is both convergent and allows to estimate the correct conditional expectation of the input…
Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences…
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.…
This work proves a new result on the correct convergence of Min-Sum Loopy Belief Propagation (LBP) in an interpolation problem on a square grid graph. The focus is on the notion of local solutions, a numerical quantity attached to each site…
A graphical model is a structured representation of locally dependent random variables. A traditional method to reason over these random variables is to perform inference using belief propagation. When provided with the true data generating…
We consider a broad class of interference coordination and resource allocation problems for wireless links where the goal is to maximize the sum of functions of individual link rates. Such problems arise in the context of, for example,…
We introduce novel belief propagation algorithms to estimate the marginals of a high dimensional probability distribution. They involve natural (co)homological constructions relevant for a localised description of statistical systems.
We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP…
Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction.…
It has been proposed by many researchers that combining deep neural networks with graphical models can create more efficient and better regularized composite models. The main difficulties in implementing this in practice are associated with…
It is well known that an arbitrary graphical model of statistical inference defined on a tree, i.e. on a graph without loops, is solved exactly and efficiently by an iterative Belief Propagation (BP) algorithm convergent to unique minimum…
We present a novel inference algorithm for arbitrary, binary, undirected graphs. Unlike loopy belief propagation, which iterates fixed point equations, we directly descend on the Bethe free energy. The algorithm consists of two phases,…
As belief networks are used to model increasingly complex situations, the need to automatically construct them from large databases will become paramount. This paper concentrates on solving a part of the belief network induction problem:…