Research

Non-Stratified Chain Event Graphs

Collaborators: Prof Jim Q. Smith

• Introduction: Chain Event Graphs (CEGs) are event-based graphical models built from trees which can topologically embed context-specific information, structural zeroes and structural missing values. They can be thought of as a generalisation of Bayesian Networks. A stratified CEG is one where the nodes corresponding to events related to the same variable are equidistant from the root node. The non-stratified class is able to represent a broader variety of real-world situations than the stratified class and in particular is useful for public health problems as they often have non-product event spaces.
• Our contribution: We develop the model class of non-stratified CEG and extended existing parameter estimation and model selection methodologies to this class. We illustrate this by modelling an intervention to reduce falls in the elderly. We further also demonstrated how this model can be queried using standard CEG methodology. In a follow-up paper, we present an algorithm to transform any staged tree, stratified or not, into a CEG. We go on to show that this transformation does not lead to any loss of information, i.e. the algorithm defines a bijective mapping from the staged tree to the CEG. This work is accompanied by documented Python code which can be found on my Github (linked below).
• Publications arising from this work:
  • Shenvi A, Smith JQ, Walton R, Eldridge S. "Modelling with Non-Stratified Chain Event Graphs." Bayesian Statistics: New Challenges and New Generations, Proceedings of BAYSM 2018. Springer
  • Shenvi A, Smith JQ. "Constructing a Chain Event Graph from a staged tree." Proceedings of Machine Learning Research, PGM 2020.
  • Related code: https://github.com/ashenvi10/Chain-Event-Graphs

Continuous Time Dynamic Chain Event Graph

Collaborators: Prof Jim Q. Smith

• Motivation: Modelling adverse recurrent events - for example falls in the elderly, asthma attacks, epileptic seizures etc - is challenging. Further, in dynamic real-world systems, temporal effects could play a large role in the evolution of the process and contribute to our understanding of the system. To study temporal effects within a system, it is important to consider the time it takes for events to occur. This motivated the development of a dynamic variant of non-stratified CEGs that can embed information about the holding/waiting/sojourn time in the various states of the process.
• Introduction: Markov models come with the implicit assumption of exponential or geometric holding times between state transitions. In several real-world applications (for example, time spent in a hospital ward) this assumption leads to unrealistic holding times. Although semi-Markov processes (SMPs) allow arbitrary holding time distributions, they are unsuitable for answering several queries which we may be interested in, such as how do the varied components of the intervention affect the outcome and for which subgroups of individuals is the intervention most beneficial? Whereas, these queries can be approached more easily using a graphical model framework. CTBNs, the continuous time variant of BNs, are a potential candidate to answer such queries but being built on top of Markov processes, they inherit the inflexibility of fixed exponential holding time distributions.
• Our contribution: We developed a novel class of dynamic CEGs called the continuous time dynamic CEG (CT-DCEG) which have an approximate SMP representation. This class benefits from being a member of the CEG and the SMP families as they are both well-developed and have several desirable properties for our application. It can embed asymmetric event-based information and allows for flexible holding time distributions. We first develop new semantics for this class and then extend conjugate parameter estimation to this class. Further we describe a special case of model selection and an exact inference algorithm for this class. We also describe how time-fixed covariates can be easily incorporated into this class. Methods are demonstrated on a longitudinal extension of the falls intervention.
• We also look at special cases of this model class: a hybrid time subclass with both discrete and continuous holding times; and a reduced subclass which conditions the analysis on the extant population through creation of an absorbing dropout state.
• Pre-prints arising from this work:
  • Shenvi A, Smith JQ. "A Bayesian Dynamic Graphical Model for Recurrent Events in Public Health."
  • Smith JQ, Shenvi A. "Assault Crime Dynamic Chain Event Graphs." Warwick repository
  • Shenvi A, Smith JQ. "Propagation for Continuous Time Chain Event Graphs."
  • Related code: https://github.com/ashenvi10/RDCEG-code

A Dynamic Latent Network Model to Identify Terrorist Cells (Turing project)

Collaborators: Dr Oliver Bunnin, Prof Jim Q. Smith

• Introduction: The threat status and criminal collaborations of potential terrorists are hidden but give rise to observable behaviours and communications. Terrorists, when acting in concert, need to communicate to organise their plots. These communications, obtained through multiple media channels of varying efficiency, inform the level of threat of suspected individuals and the extent of collaboration between these individuals. The authorities need to allocate their limited resources to monitor these suspected individuals in a suitable way to identify terrorist cells that might be collaborating to orchestrate a terrorist attack with possibly devastating consequences.
• Our contribution: We develop a dynamic latent network model that integrates communications obtained from various channels in realtime with prior knowledge the authorities have on suspected individuals. My contribution to this project was in terms of model development. The topology and edge weights for the fellowship network of collaboration between pairs of individuals are informed by a multivariate hidden Markov model which uses a Bayesian steady model development over time. Further, we demonstrate how, by assuming certain plausible conditional independences across the measurements associated with this population, the network model can be combined with models of individual suspects to provide fast transparent algorithms to predict group attacks.

• Pre-prints arising from this work:
  • Bunnin FO, Shenvi A, Smith JQ. "Network Modelling of Criminal Collaborations with Dynamic Bayesian Steady Evolutions."

Bayesian Mixture Modelling approach to CEG Model Selection (Turing project)

Collaborators: Dr Silvia Liverani

• Introduction: A CEG are obtained by transforming its underlying event tree. This transformation has an intermediate construction of a staged tree. Two vertices are in the same stage in an event tree when, in non-technical terms, their one step ahead evolution is equivalent. A staged tree is obtained from an event tree by colouring the vertices according to their stage memberships. Each distinct CEG has a unique staged tree. Hence, CEG model selection is primarily about identifying the stage partitions among the set of vertices of the event tree.
• Our contribution: The model selection problem above can be framed as a mixture modelling problem where each stage can be thought of as a mixture component. The benefits of framing the problem in this way is that we do not need to rely on conjugate exponential families for describing holding times in CT-DCEGs. We demonstrate how CEG model selection through the mixture modelling approach can be easily coded up using Stan software wrapped in R.

• Manuscript in preparation for this work:
  • Shenvi A, Liverani S. "CEG Model Selection with Mixture Models".

Other work:

• Supported model development and manuscript preparation for a Bayesian decision support system for comparing COVID-19 policies.
  • Pre-print: Strong P, Shenvi A, Yu X, Papamichail N, Wynn HP, Smith JQ. "Decision Support for COVID-19 Policy Including Poverty Drivers."
• Aided in the causal analysis in a game app designed to help individuals in their smoking cessation efforts.
  • Publication: Edwards EA, Caton H, Lumsden J, Rivas C, Steed L, Pirunsarn Y, Jumbe S, Newby C, Shenvi A, Mazumdar S, Smith JQ. "Creating a Theoretically Grounded, Gamified Health App: Lessons From Developing the Cigbreak Smoking Cessation Mobile Phone Game." JMIR serious games. 2018 Oct;6(4).

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Email: A.Shenvi@warwick.ac.uk

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