Related papers: Belief Optimization for Binary Networks: A Stable …
Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…
Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a…
Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Many network applications are based on binary-state networks, where each component has one of two states: success or failure. Efficient algorithms to evaluate binary-state network reliability are continually being developed. Reliability…
Belief propagation has recently emerged as a powerful framework for evaluating tensor networks in higher dimensions, combining computational efficiency with provable analytical guarantees. In this work, we develop the first end-to-end…
In Bayesian networks, exact belief propagation is achieved through message passing algorithms. These algorithms (ex: inward and outward) provide only a recursive definition of the corresponding messages. In contrast, when working on hidden…
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 illustrate the utility of the recently developed loop calculus for improving the Belief Propagation (BP) algorithm. If the algorithm that minimizes the Bethe free energy fails we modify the free energy by accounting for a critical loop…
In 1999, Brodal and Fagerberg (BF) gave an algorithm for maintaining a low outdegree orientation of a dynamic uniformly sparse graph. Specifically, for a dynamic graph on $n$-vertices, with arboricity bounded by $\alpha$ at all times, the…
A comprehensive picture of three Bethe-Kikuchi variational principles including their relationship to belief propagation (BP) algorithms on hypergraphs is given. The structure of BP equations is generalized to define continuous-time…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real…
We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming relaxation of the problem has no fractional solutions, then the cavity or belief propagation…
In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified message-passing algorithm architecture. We generalize the…
Max-product "belief propagation" is an iterative, local, message-passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success…
Graph neural network models have been extensively used to learn node representations for graph structured data in an end-to-end setting. These models often rely on localized first order approximations of spectral graph convolutions and…
Consider a Bayesian binary decision-making problem in star networks, where local agents make selfish decisions independently, and a fusion agent makes a final decision based on aggregated decisions and its own private signal. In particular,…
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.
This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of…