Related papers: Belief Propagation, Bethe Approximation and Polyno…

This paper considers the problem of tracking a large-scale number of group targets. Usually, multi-target in most tracking scenarios are assumed to have independent motion and are well-separated. However, for group target tracking (GTT),…

In this paper we show how graph structure can be used to drastically reduce the computational bottleneck of the Breadth First Search algorithm (the foundation of many graph traversal techniques). In particular, we address parallel…

Most of the successful deep neural network architectures are structured, often consisting of elements like convolutional neural networks and gated recurrent neural networks. Recently, graph neural networks have been successfully applied to…

The study of Markov processes and broadcasting on trees has deep connections to a variety of areas including statistical physics, graphical models, phylogenetic reconstruction, Markov Chain Monte Carlo, and community detection in random…

The Bethe Ansatz provides exact solutions for certain interacting quantum many-body systems, yet its success is confined to narrow regimes and breaks down abruptly outside them. Despite extensive developments in integrable systems, a…

The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…

Near optimal decoding of good error control codes is generally a difficult task. However, for a certain type of (sufficiently) good codes an efficient decoding algorithm with near optimal performance exists. These codes are defined via a…

We propose a hybrid message passing method for distributed cooperative localization and tracking of mobile agents. Belief propagation and mean field message passing are employed for, respectively, the motion-related and measurement-related…

This paper explores the use of factor graphs as an inference and analysis tool for Bayesian peer-to-peer decentralized data fusion. We propose a framework by which agents can each use local factor graphs to represent relevant partitions of…

Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…

Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an…

A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…

The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is…

The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem…

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…

Community partition is of great importance in social networks because of the rapid increasing network scale, data and applications. We consider the community partition problem under LT model in social networks, which is a combinatorial…

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…

We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work…