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Weak convergence of joint distributions generally does not imply convergence of conditional distributions. In particular, conditional distributions need not converge when joint Gaussian distributions converge to a singular Gaussian limit.…

Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…

A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among…

Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We…

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…

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

We prove theorems about the Gaussian asymptotics of an empirical bridge built from linear model regressors with multiple regressor ordering. We study the testing of the hypothesis of a linear model for the components of a random vector: one…

We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…

The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full generality have been unsuccessful to date, numerous partial…

Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…

Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…

Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under…

Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…

A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…

Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…

The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential…

We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best…

Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict…

We are interested in modeling networks in which the connectivity among the nodes and node attributes are random variables and interact with each other. We propose a probabilistic model that allows one to formulate jointly a probability…

Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…