Related papers: Matrix representations and independencies in direc…

In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations.…

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…

With the aid of the concept of stable independence we can construct, in an efficient way, a compact representation of a semi-graphoid independence relation. We show that this representation provides a new necessary condition for the…

Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for…

This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also…

In this paper, we employ the decomposition of a directed network as an undirected graph plus its associated node metadata to characterise the cyclic structure found in directed networks by finding a Minimal Cycle Basis of the undirected…

Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing universal properties of conditional independence. Categoroids are…

The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size. Two graphs are said to be \textit{independence equivalent} if they have equivalent independence polynomials. We extend…

We describe a graphical model for probabilistic relationships---an alternative to the Bayesian network---called a dependency network. The graph of a dependency network, unlike a Bayesian network, is potentially cyclic. The probability…

Scientists often use directed acyclic graphs (days) to model the qualitative structure of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which…

The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third…

The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…

Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables.…

A main question in graphical models and causal inference is whether, given a probability distribution $P$ (which is usually an underlying distribution of data), there is a graph (or graphs) to which $P$ is faithful. The main goal of this…

Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…

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…

Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…

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…

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…