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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…
For the minimum cardinality vertex cover and maximum cardinality matching problems, the max-product form of belief propagation (BP) is known to perform poorly on general graphs. In this paper, we present an iterative loopy annealing BP…
There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…
Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion…
Belief propagation -- a powerful heuristic method to solve inference problems involving a large number of random variables -- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Belief Propagation algorithms are instruments used broadly to solve graphical model optimization and statistical inference problems. In the general case of a loopy Graphical Model, Belief Propagation is a heuristic which is quite successful…
In order to diminish the damaging effect of loops on belief propagation (BP), the first explicit version of generalized BP for networks, the KCN-method, was recently introduced. Despite its success, the KCN-method spends computational…
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…
We study the Maximum Weight Matching (MWM) problem for general graphs through the max-product Belief Propagation (BP) and related Linear Programming (LP). The BP approach provides distributed heuristics for finding the Maximum A Posteriori…
How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels…
Location-aware networks will introduce innovative services and applications for modern convenience, applied ocean sciences, and public safety. In this paper, we establish a hybrid method for model-based and data-driven inference. We…
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…
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…
Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the Belief Propagation solution. By adding correction terms…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
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.…
The cluster variation method has been developed into a general theoretical framework for treating short-range correlations in many-body systems after it was first proposed by Kikuchi in 1951. On the numerical side, a message-passing…
We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions…