Related papers: Generalized Belief Propagation on Tree Robust Stru…

Given a graph whose edges are labeled by ideals of a commutative ring R with identity, a generalized spline is a vertex labeling by the elements of R such that the difference of the labels on adjacent vertices lies in the ideal associated…

It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…

We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the trees. Through a bijection between plane…

Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…

A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…

An integer generalized spline is a set of vertex labels on an edge-labeled graph that satisfy the condition that if two vertices are joined by an edge, the vertex labels are congruent modulo the edge label. Foundational work on these…

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…

Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…

Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can…

Graph neural networks (GNNs) have been widely used to predict properties and heuristics of mixed-integer linear programs (MILPs) and hence accelerate MILP solvers. This paper investigates the capacity of GNNs to represent strong branching…

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

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…

The increasing complexity of cascading risks in urban systems necessitates robust, data-driven frameworks to model interdependencies across multiple domains. This study presents a foundational Bayesian network-based approach for analyzing…

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…

With the wide-spread availability of complex relational data, semi-supervised node classification in graphs has become a central machine learning problem. Graph neural networks are a recent class of easy-to-train and accurate methods for…

Machine learning based approaches are being increasingly used for designing decoders for next generation communication systems. One widely used framework is neural belief propagation (NBP), which unfolds the belief propagation (BP)…

A class of models that have been widely used are the exponential random graph (ERG) models, which form a comprehensive family of models that include independent and dyadic edge models, Markov random graphs, and many other graph…

Inference in continuous label Markov random fields is a challenging task. We use particle belief propagation (PBP) for solving the inference problem in continuous label space. Sampling particles from the belief distribution is typically…

We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the…