Causal discovery through MAP selection of stratified chain event graphs

Abstract

This is the published version of the paper.This version of the publication may differ from the final published version. Abstract: 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. Permanent repository link

Equivalence classes of staged trees

“…This is because no composition of the swaps on the twins can form a level-swap on (S, θ S ). So a model which treats life events as an explanatory variable of the response variable hospital admission as in the study [2] is less supported by the data than one treating hospitalisation as an explanatory variable of life events as in [5]. Note that no deductions about an ordering of variables would have been possible within the original BN representation of the data because the MAP model turns out to be decomposable.…”

“…To apply this principle, it is essential to know when two CEGs make the same distributional assertions. The third reason is inferential: just like a Bayesian network (BN), a CEG or staged tree has a natural causal extension [5,24]. So, in particular, causal discovery algorithms can be applied to CEGs to elicit a putative causal ordering between various associated variables.…”

“…The staged tree (T , θ T ) in Fig. 4a was found using an MAP search [5]. We will now apply Theorem 1 to the statistical equivalence class [T , θ T ] in order to enrich our understanding of the model P (T ,θT ) represented by that tree.…”

Proof and Uncertainty in Causal Claims

“…In particular, we now have a suite of tools that allow us to fully explore chain event graphs (CEGs). Cowell and Smith (2014) develop causal discovery techniques to find the best fitting CEG from data. Thwaites et al (2010) demonstrated how the causal hypotheses of a CEG offer a profound flexibility.…”

A graphical method for simplifying Bayesian games

“…It provides a platform from which to deduce dependence relationships between variables directly from the graph's topology. CEGs have principally been used for learning/model selection (see for example [21,2]), but also in two areas of interest to us in this paper -causal analysis (see for example [30,7]), and also decision analysis [29] where the semantics of the CEG can be extended to provide algorithms which allow users to discover minimal sets of variables needed to fully specify an SEUM decision rule. In 2015 it was realised that CEGs include Acyclic Probabilistic Finite Automata (APFAs) as a special case [8].…”