Related papers: Characterizations of Decomposable Dependency Model…

In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…

The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential…

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without…

Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…

This paper discusses causal independence models and a generalization of these models called causal interaction models. Causal interaction models are models that have independent mechanisms where a mechanism can have several causes. In…

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…

In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…

For a given discrete decomposable graphical model, we identify several alternative parametrizations, and construct the corresponding reference priors for suitable groupings of the parameters. Specifically, assuming that the cliques of the…

An important problem in biological modeling is choosing the right model. Given experimental data, one is supposed to find the best mathematical representation to describe the real-world phenomena. However, there may not be a unique model…

Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…

Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information…

This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is…

Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…

Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this…

Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…

We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to…

Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two…

Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…

Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…

A network provides powerful means of representing complex relationships between entities by abstracting entities as vertices, and relationships as edges connecting vertices in a graph. Beyond the presence or absence of relationships, a…