Related papers: Nishimori meets Bethe: a spectral method for node …
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling…
We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the…
This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…
Using the Bethe ansatz analysis as was reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly…
We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…
Graphs are useful to interpret widely used image processing methods, e.g., bilateral filtering, or to develop new ones, e.g., kernel based techniques. However, simple graph constructions are often used, where edge weight and connectivity…
We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
We have constructed a Bayesian neural network able of retrieving tropospheric temperature profiles from rotational Raman-scatter measurements of nitrogen and oxygen and applied it to measurements taken by the RAman Lidar for Meteorological…
We introduce an approach for solving PDEs over manifolds using physics informed neural networks whose architecture aligns with spectral methods. The networks are trained to take in as input samples of an initial condition, a time stamp and…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
We apply estimation theory to a system formed by two interacting trapped ions. By using the Fisher matrix formalism, we introduce a simple scheme for estimation of the temperature of the longitudinal vibrational modes of the ions. We use…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
Machine learning, and representation learning in particular, has the potential to facilitate drug discovery by screening a large chemical space in silico. A successful approach for representing molecules is to treat them as a graph and…
We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree $d$ for large constant $d$, proving that when the normalized inverse temperature satisfies $\beta>1$ (asymptotically…
In order to conduct analyses of networked systems where connections between individuals take on a range of values - counts, continuous strengths or ordinal rankings - a common technique is to dichotomize the data according to their…
Motivated by inferring cellular signaling networks using noisy flow cytometry data, we develop procedures to draw inference for Bayesian networks based on error-prone data. Two methods for inferring causal relationships between nodes in a…