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Maximal ancestral graphs (MAGs) have many desirable properties; in particular they can fully describe conditional independences from directed acyclic graphs (DAGs) in the presence of latent and selection variables. However, different MAGs…
Let $X$ be a max-stable random vector with positive continuous density. It is proved that the conditional independence of any collection of disjoint sub-vectors of $X$ given the remaining components implies their joint independence. We…
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…
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…
Pearls concept OF a d - connecting path IS one OF the foundations OF the modern theory OF graphical models : the absence OF a d - connecting path IN a DAG indicates that conditional independence will hold IN ANY distribution factorising…
We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…
Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for…
Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We…
We study submodels of Gaussian DAG models defined by partial homogeneity constraints imposed on the model error variances and structural coefficients. We represent these models with colored DAGs and investigate their properties for use in…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…
Building higher-dimensional copulas is generally recognized as a difficult problem. Regular-vines using bivariate copulas provide a flexible class of high-dimensional dependency models. In large dimensions, the drawback of the model is the…
Estimation of the conditional independence graph (CIG) of high-dimensional multivariate Gaussian time series from multi-attribute data is considered. Existing methods for graph estimation for such data are based on single-attribute models…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…
A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…