Related papers: Marginalization and Conditioning for LWF Chain Gra…
In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables…
Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…
Depending on the interpretation of the type of edges, a chain graph can represent different relations between variables and thereby independence models. Three interpretations, known by the acronyms LWF, MVR, and AMP, are prevalent.…
Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation criterion), and the local…
The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous…
Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the…
Any regular Gaussian probability distribution that can be represented by an AMP chain graph (CG) can be expressed as a system of linear equations with correlated errors whose structure depends on the CG. However, the CG represents the…
Graph data structures are fundamental for studying connected entities. With an increase in the number of applications where data is represented as graphs, the problem of graph generation has recently become a hot topic. However, despite its…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a…
Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…
Semi-supervised node classification on graph-structured data has many applications such as fraud detection, fake account and review detection, user's private attribute inference in social networks, and community detection. Various methods…
Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs…
This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…
We address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes…
Federated graph learning (FGL) enables multiple clients to collaboratively train powerful graph neural networks without sharing their private, decentralized graph data. Inherited from generic federated learning, FGL is critically challenged…
We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed…
This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover,…