Related papers: Parameter Priors for Directed Acyclic Graphical Mo…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…
In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modeling of such different data-types, based on global parameters consisting of a directed acyclic…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix…
Let $\mathbf{W}$ be a correlated complex non-central Wishart matrix defined through $\mathbf{W}=\mathbf{X}^H\mathbf{X}$, where $\mathbf{X}$ is $n\times m \, (n\geq m)$ complex Gaussian with non-zero mean $\boldsymbol{\Upsilon}$ and…
We consider the problem of recovering the true causal structure among a set of variables, generated by a linear acyclic structural equation model (SEM) with the error terms being independent, not necessarily Gaussian, and having equal…
The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
We present a graphical criterion for covariate adjustment that is sound and complete for four different classes of causal graphical models: directed acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially directed…
Bayesian methods constitute a popular approach for estimating the conditional independence structure in Gaussian graphical models, since they can quantify the uncertainty through the posterior distribution. Inference in this framework is…
We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…
We consider the random geometric graph on $n$ vertices drawn uniformly from a $d$--dimensional sphere. We focus on the sparse regime, when the expected degree is constant independent of $d$ and $n$. We show that, when $d$ is larger than $n$…
We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…
The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
The Wishart model for real symmetric correlation matrices is defined as $\mathsf{W}=\mathsf{AA}^{t}$, where matrix $\mathsf{A}$ is usually a rectangular Gaussian random matrix and $\mathsf{A}^{t}$ is the transpose of $\mathsf{A}$.…
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…
Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional…
We define Gaussian graphical models on directed acyclic graphs with coloured vertices and edges, calling them RDAG (restricted directed acyclic graph) models. If two vertices or edges have the same colour, their parameters in the model must…
Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest.…