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We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…

Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables.…

In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical…

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid…

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…

Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that…

Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful…

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…

We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks…

We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a…

Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common…

Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…

Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first…

We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…

We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by…

For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class…

This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…