Related papers: A Separation Theorem for Chain Event Graphs
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
Chain Event Graphs (CEGs) are a recent family of probabilistic graphical models - a generalisation of Bayesian Networks - providing an explicit representation of structural zeros, structural missing values and context-specific conditional…
The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the well-known d-separation criterion. It allows us to build graphical representations of dependency models (usually probabilistic…
Chain Event Graphs are probabilistic graphical models designed especially for the analysis of discrete statistical problems which do not admit a natural product space structure. We show here how they can be used for decision analysis, and…
Recent works show that the graph structure of sentences, generated from dependency parsers, has potential for improving event detection. However, they often only leverage the edges (dependencies) between words, and discard the dependency…
Graph Neural Networks (GNNs) are effective for node classification in graph-structured data, but they lack explainability, especially at the global level. Current research mainly utilizes subgraphs of the input as local explanations or…
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…
Bayesian networks (BNs) are used for inference and sampling by exploiting conditional independence among random variables. Context specific independence (CSI) is a property of graphical models where additional independence relations arise…
An efficient algorithm is developed that identifies all independencies implied by the topology of a Bayesian network. Its correctness and maximality stems from the soundness and completeness of d-separation with respect to probability…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
Chain event graphs have been established as a practical Bayesian graphical tool. While bespoke diagnostics have been developed for Bayesian Networks, they have not yet been defined for the statistical class of Chain Event Graph models.…
Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random…
We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network $\mathcal{M}$ on a graph with $n$ discrete variables and bounded in-degree and bounded `confounded…
The Dynamic Chain Event Graph (DCEG) is able to depict many classes of discrete random processes exhibiting asymmetries in their developments and context-specific conditional probabilities structures. However, paradoxically, this very…
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…
The graph of a Bayesian Network (BN) can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would…
Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how…
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…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…