An N Time-Slice Dynamic Chain Event Graph
This work addresses a specific problem for graphical modellers in statistics and machine learning by providing a more feasible and implementable subclass of DCEGs, though it is incremental as it builds on existing DCEG theory.
The paper tackles the limited application of Dynamic Chain Event Graphs (DCEGs) by developing an object-oriented method to analyze a new subclass called the N Time-Slice DCEG (NT-DCEG), relating it to Markov processes and enabling context-specific independence checks, as illustrated with examples of inmate radicalization in prisons.
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 generality has so far frustrated its wide application. So in this paper we develop an object-oriented method to fully analyse a particularly useful and feasibly implementable new subclass of these graphical models called the N Time-Slice DCEG (NT-DCEG). After demonstrating a close relationship between an NT-DCEG and a specific class of Markov processes, we discuss how graphical modellers can exploit this connection to gain a deep understanding of their processes. We also show how to read from the topology of this graph context-specific independence statements that can then be checked by domain experts. Our methods are illustrated throughout using examples of dynamic multivariate processes describing inmate radicalisation in a prison.