Related papers: Marginal AMP Chain Graphs
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
Ancestral graphs can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any ancestral graph, there may be several other graphs to which it is Markov…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
In graphical modelling, a bi-directed graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bi-directed graph into a maximal ancestral graph that (i)…
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present the first method for fitting these…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with…
The invariance properties of interventional distributions relative to the observational distribution, and how these properties allow us to refine Markov equivalence classes (MECs) of DAGs, is central to causal DAG discovery algorithms that…
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…
Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…
This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models…
Directed acyclic graphs (DAGs) can be characterised as directed graphs whose strongly connected components are isolated vertices. Using this restriction on the strong components, we discover that when $m = cn$, where $m$ is the number of…
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
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…