Modelling with non-stratified chain event graphs

© 2019, Springer Nature Switzerland AG. Chain Event Graphs (CEGs) are recent probabilistic graphical modelling tools that have proved successful in modelling scenarios with context-specific independencies. Although the theory underlying CEGs supports appropriate representation of structural zeroes, the literature so far does not provide an adaptation of the vanilla CEG methods for a real-world application presenting structural zeroes also known as the non-stratified CEG class. To illustrate these methods, we present a non-stratified CEG representing a public health intervention designed to reduce the risk and rate of falling in the elderly. We then compare the CEG model to the more conventional Bayesian Network model when applied to this setting

Equivalence Classes of Staged Trees

In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.Comment: 18 pages, 4 figure

cegpy: Modelling with Chain Event Graphs in Python

Chain event graphs (CEGs) are a recent family of probabilistic graphical models that generalise the popular Bayesian networks (BNs) family. Crucially, unlike BNs, a CEG is able to embed, within its graph and its statistical model, asymmetries exhibited by a process. These asymmetries might be in the conditional independence relationships or in the structure of the graph and its underlying event space. Structural asymmetries are common in many domains, and can occur naturally (e.g. a defendant vs prosecutor's version of events) or by design (e.g. a public health intervention). However, there currently exists no software that allows a user to leverage the theoretical developments of the CEG model family in modelling processes with structural asymmetries. This paper introduces cegpy, the first Python package for learning and analysing complex processes using CEGs. The key feature of cegpy is that it is the first CEG package in any programming language that can model processes with symmetric as well as asymmetric structures. cegpy contains an implementation of Bayesian model selection and probability propagation algorithms for CEGs. We illustrate the functionality of cegpy using a structurally asymmetric dataset

The R Package stagedtrees for Structural Learning of Stratified Staged Trees

stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to plot the models and perform inference. The capabilities of stagedtrees are illustrated using mainly two datasets both included in the package or bundled in R

A New Method for tackling Asymmetric Decision Problems

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 through designation of some nodes as decision nodes, and the addition of utilities. We provide a local propagation algorithm for finding an optimal decision strategy and maximising expected utility. We also compare CEGs with Influence diagrams, Valuation Networks, Sequential decision diagrams, Sequential influence diagrams and Decision circuits for the representation and analysis of asymmetric decision problems

Causal discovery through MAP selection of stratified chain event graphs

We introduce a subclass of chain event graphs that we call stratified chain event graphs, and present a dynamic programming algorithm for the optimal selection of such chain event graphs that maximizes a decomposable score derived from a complete independent sample. We apply the algorithm to such a dataset, with a view to deducing the causal structure of the variables under the hypothesis that there are no unobserved confounders. We show that the algorithm is suitable for small problems. Similarities with and differences to a dynamic programming algorithm for MAP learning of Bayesian networks are highlighted, as are the relations to causal discovery using Bayesian networks