Related papers: A Separation Theorem for Chain Event Graphs
We extend the decomposition approach for learning Bayesian networks (BNs) proposed by (Xie et. al.) to learning multivariate regression chain graphs (MVR CGs), which include BNs as a special case. The same advantages of this decomposition…
A Bayesian Network is a directed acyclic graph (DAG) on a set of $n$ random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite…
Chain event graphs are a family of probabilistic graphical models that generalise Bayesian networks and have been successfully applied to a wide range of domains. Unlike Bayesian networks, these models can encode context-specific…
Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners…
The graphical structure of Probabilistic Graphical Models (PGMs) encodes the conditional independence (CI) relations that hold in the modeled distribution. Graph algorithms, such as d-separation, use this structure to infer additional…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…
Entity interaction prediction is essential in many important applications such as chemistry, biology, material science, and medical science. The problem becomes quite challenging when each entity is represented by a complex structure,…
This paper explores the role of Directed Acyclic Graphs (DAGs) as a representation of conditional independence relationships. We show that DAGs offer polynomially sound and complete inference mechanisms for inferring conditional…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…
The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent…
The assumption that data samples are independent and identically distributed (iid) is standard in many areas of statistics and machine learning. Nevertheless, in some settings, such as social networks, infectious disease modeling, and…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
A Bayesian Belief Network (BN) is a model of a joint distribution over a setof n variables, with a DAG structure to represent the immediate dependenciesbetween the variables, and a set of parameters (aka CPTables) to represent thelocal…
Functional causal models (fCMs) specify functional dependencies between random variables associated to the vertices of a graph. In directed acyclic graphs (DAGs), fCMs are well-understood: a unique probability distribution on the random…
Shenoy and Shafer {Shenoy:90} demonstrated that both for Dempster-Shafer Theory and probability theory there exists a possibility to calculate efficiently marginals of joint belief distributions (by so-called local computations) provided…
Graph Neural Networks achieve remarkable results on problems with structured data but come as black-box predictors. Transferring existing explanation techniques, such as occlusion, fails as even removing a single node or edge can lead to…
Interacting systems of events may exhibit cascading behavior where events tend to be temporally clustered. While the cascades themselves may be obvious from the data, it is important to understand which states of the system trigger them.…
The class of chain event graph models is a generalisation of the class of discrete Bayesian networks, retaining most of the structural advantages of the Bayesian network for model interrogation, propagation and learning, while more…
Estimation of the conditional independence graph (CIG) of high-dimensional multivariate Gaussian time series from multi-attribute data is considered. Existing methods for graph estimation for such data are based on single-attribute models…