Related papers: Markov Equivalence Classes for Maximal Ancestral G…
Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper…
Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…
Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…
Principled reasoning about the identifiability of causal effects from non-experimental data is an important application of graphical causal models. This paper focuses on effects that are identifiable by covariate adjustment, a commonly used…
Directed acyclic graphical models (DAGs) are often used to describe common structural properties in a family of probability distributions. This paper addresses the question of classifying DAGs up to an isomorphism. By considering Gaussian…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that…
We consider the problem of learning causal Directed Acyclic Graphs (DAGs) using combinations of observational and interventional experimental data. Current methods tailored to this setting assume that interventions either destroy…
We present a new, efficient procedure to establish Markov equivalence between directed graphs that may or may not contain cycles under the \textit{d}-separation criterion. It is based on the Cyclic Equivalence Theorem (CET) in the seminal…
We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a…
Besides the need for a better understanding of networks, there is a need for prescriptive models and tools to specify requirements concerning networks and their associated graph representations. We propose class-based graphs as a means to…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
We consider the graph class Grounded-L corresponding to graphs that admit an intersection representation by L-shaped curves, where additionally the topmost points of each curve are assumed to belong to a common horizontal line. We prove…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Markov networks are probabilistic graphical models that employ undirected graphs to depict conditional independence relationships among variables. Our focus lies in constraint-based structure learning, which entails learning the undirected…
This paper introduces graphemes for constructing and analyzing stochastic processes that describe the evolution of large dynamic graphs. Unlike graphons, which capture the static properties of dense graphs via exchangeability or subgraph…
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…
Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with…
We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that…
The degree matrix of a graph is the diagonal matrix with diagonal entries equal to the degrees of the vertices of $X$. If $X_1$ and $X_2$ are graphs with respective adjacency matrices $A_1$ and $A_2$ and degree matrices $D_1$ and $D_2$, we…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…