Related papers: Detection of Gauss-Markov Random Fields with Neare…

Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a…

The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have been widely used to accommodate spatial dependence under the generalized linear mixed model framework. These models have limitations rooted in the symmetry and…

Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…

Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large…

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…

In high-dimensional graph learning problems, some topological properties of the graph, such as bounded node degree or tree structure, are typically assumed to hold so that the sample complexity of recovering the graph structure can be…

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network…

We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…

A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…

Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised…

The problem of scheduling sensor transmissions for the detection of correlated random fields using spatially deployed sensors is considered. Using the large deviations principle, a closed-form expression for the error exponent of the miss…

Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…

We derive the distribution of the maximum number of common neighbours of a pair of vertices in a dense random regular graph.The proof involves two important steps. One step is to establish the extremal independence property: the asymptotic…

Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…

Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the…

In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…

We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…

This paper introduces a new framework to study the asymptotical behavior of the empirical distribution function (e.d.f.) of Gaussian vector components, whose correlation matrix $\Gamma^{(m)}$ is dimension-dependent. Hence, by contrast with…

This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…

This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1}…