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A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…
This paper investigates the problem of graph signal recovery (GSR) when the topology of the graph is not known in advance. In this paper, the elements of the weighted adjacency matrix is statistically related to normal distribution and the…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…
Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's…
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivotal role. While models such as Whittle-Mat\'ern fields have…
Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the…
Neural rendering techniques have made substantial progress in generating photo-realistic 3D scenes. The latest 3D Gaussian Splatting technique has achieved high quality novel view synthesis as well as fast rendering speed. However, 3D…
Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting structure has a natural metric that allows for the study of…
Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional…
We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Mat\'ern fields, are defined via a fractional stochastic differential equation on the compact metric…
We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
Reconstructing open surfaces from multi-view images is vital in digitalizing complex objects in daily life. A widely used strategy is to learn unsigned distance functions (UDFs) by checking if their appearance conforms to the image…