Related papers: Message Passing and Combinatorial Optimization
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to…
We introduce a new type of graphical model that we call a "memory factor network" (MFN). We show how to use MFNs to model the structure inherent in many types of data sets. We also introduce an associated message-passing style algorithm…
We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms are based on contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is…
The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the…
Message passing equations yield a sharp percolation transition in finite graphs, as an artifact of the locally treelike approximation. For an arbitrary finite, connected, undirected graph we construct an infinite tree having the same local…
Graphs have been widely used to represent complex data in many applications. Efficient and effective analysis of graphs is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO)…
Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard,…
A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve…
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…
Belief Propagation (BP) is a popular, distributed heuristic for performing MAP computations in Graphical Models. BP can be interpreted, from a variational perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to solve…
We consider a class of spreading processes on networks, which generalize commonly used epidemic models such as the SIR model or the SIS model with a bounded number of re-infections. We analyse the related problem of inference of the…
Despite recent advances in achieving fair representations and predictions through regularization, adversarial debiasing, and contrastive learning in graph neural networks (GNNs), the working mechanism (i.e., message passing) behind GNNs…
Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is…
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…
We present a "pull" approach to approximate products of Gaussian mixtures within message updates for Nonparametric Belief Propagation (NBP) inference. Existing NBP methods often represent messages between continuous-valued latent variables…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…
Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which…
Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…
In this paper we offer a solution to a long-standing problem in the study of networks. Message passing is a fundamental technique for calculations on networks and graphs. The first versions of the method appeared in the 1930s and over the…