Event-Driven Continuous Time Bayesian Networks

We introduce a novel event-driven continuous time Bayesian network (ECTBN) representation to model situations where a system's state variables could be influenced by occurrences of events of various types. In this way, the model parameters and graphical structure capture not only potential “causal” dynamics of system evolution but also the influence of event occurrences that may be interventions. We propose a greedy search procedure for structure learning based on the BIC score for a special class of ECTBNs, showing that it is asymptotically consistent and also effective for limited data. We demonstrate the power of the representation by applying it to model paths out of poverty for clients of CityLink Center, an integrated social service provider in Cincinnati, USA. Here the ECTBN formulation captures the effect of classes/counseling sessions on an individual's life outcome areas such as education, transportation, employment and financial education.

Continuous Time Bayesian Networks in Prognosis and Health Management of Centrifugal Pumps

This paper presents a novel method for performing risk-based prognosis and health management (rPHM) on centrifugal pumps. We present the rPHM framework and apply common modeling tools used in reliability and testability analysis---dependency (D) matrices and fault tree analysis---as a basis for constructing an underlying predictive model. We then introduce the mathematics of the Continuous Time Bayesian Network (CTBN), which is a probabilistic graphical model based on a factored Markov process that is designed to capture system evolution through time, and we explain how to apply a CTBN derived from D-matrices and fault trees to consider the impact of a set of faults common to centrifugal pumps on emerging hazards in the pump system. We demonstrate the utility of using CTBNs for rPHM analysis with two experiments showing the descriptive power of our modeling approach.

Learning Continuous Time Bayesian Networks in Non-stationary Domains

Non-stationary continuous time Bayesian networks are introduced. They allow the parents set of each node in a continuous time Bayesian network to change over time. Structural learning of nonstationary continuous time Bayesian networks is developed under different knowledge settings. A macroeconomic dataset is used to assess the effectiveness of learning non-stationary continuous time Bayesian networks from real-world data.

Tutorial on Structured Continuous-Time Markov Processes

A continuous-time Markov process (CTMP) is a collection of variables indexed by a continuous quantity, time. It obeys the Markov property that the distribution over a future variable is independent of past variables given the state at the present time. We introduce continuous-time Markov process representations and algorithms for filtering, smoothing, expected sufficient statistics calculations, and model estimation, assuming no prior knowledge of continuous-time processes but some basic knowledge of probability and statistics. We begin by describing "flat" or unstructured Markov processes and then move to structured Markov processes (those arising from state spaces consisting of assignments to variables) including Kronecker, decision-diagram, and continuous-time Bayesian network representations. We provide the first connection between decision-diagrams and continuous-time Bayesian networks.