Related papers: Generalized Belief Propagation on Tree Robust Stru…

GBP and EP are two successful algorithms for approximate probabilistic inference, which are based on different approximation strategies. An open problem in both algorithms has been how to choose an appropriate approximation structure. We…

Inspired by the success of large language models, there is a trend toward developing graph foundation models to conduct diverse downstream tasks in various domains. However, current models often require extra fine-tuning to apply their…

Knowledge graph (KG) embedding methods learn geometric representations of entities and relations to predict plausible missing knowledge. These representations are typically assumed to capture rule-like inference patterns. However, our…

Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…

We present a framework to cluster nodes in directed networks according to their roles by combining Role-Based Similarity (RBS) and Markov Stability, two techniques based on flows. First we compute the RBS matrix, which contains the pairwise…

We consider the problem of maximum likelihood estimation in linear models represented by factor graphs and solved via the Gaussian belief propagation algorithm. Motivated by massive internet of things (IoT) networks and edge computing, we…

In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…

We consider a probability measure on cycle-rooted spanning forests (CRSFs) introduced by Kenyon. CRSFs are spanning subgraphs, each connected component of which has a unique cycle; they generalize spanning trees. A generalization of…

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…

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,…

The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…

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 Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…

We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are…

Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with…

The generalization error of deep neural networks via their classification margin is studied in this work. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary non-linearities…

Tree ensemble algorithms as RandomForest and GradientBoosting are currently the dominant methods for modeling discrete or tabular data, however, they are unable to perform a hierarchical representation learning from raw data as…

A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…

We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs).…

The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…