Related papers: Message Passing and Combinatorial Optimization

While Graph Neural Networks (GNNs) have achieved remarkable success, their design largely relies on empirical intuition rather than theoretical understanding. In this paper, we present a comprehensive analysis of GNN behavior through three…

Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…

We consider a number of fundamental statistical and graph problems in the message-passing model, where we have $k$ machines (sites), each holding a piece of data, and the machines want to jointly solve a problem defined on the union of the…

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…

In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special…

The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a…

We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…

We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly…

One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…

In this paper, we present structured message passing (SMP), a unifying framework for approximate inference algorithms that take advantage of structured representations such as algebraic decision diagrams and sparse hash tables. These…

Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…

Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…

We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as inference problems…

Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple…

We introduce the lifted Generalized Belief Propagation (GBP) message passing algorithm, for the computation of sum-product queries in Probabilistic Relational Models (e.g. Markov logic network). The algorithm forms a compact region graph…

An improved inference method for densely connected systems is presented. The approach is based on passing condensed messages between variables, representing macroscopic averages of microscopic messages. We extend previous work that showed…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

Strategies to improve the predicting performance of Message-Passing Neural-Networks for molecular property predictions can be achieved by simplifying how the message is passed and by using descriptors that capture multiple aspects of…

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,…

Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural…