Continuous Time Bayesian Networks

TL;DR

This paper introduces a language for finite state continuous time Bayesian networks (CTBNs) that model structured stochastic processes evolving over continuous time, allowing for complex temporal probabilistic reasoning.

Contribution

The paper formalizes a new language for CTBNs, providing semantics, inference algorithms, and addressing computational challenges in modeling continuous-time stochastic processes.

Findings

Defined a probabilistic semantics for CTBNs

Developed an approximate inference algorithm leveraging process structure

Discussed computational difficulties in exact inference

Abstract

In this paper we present a language for finite state continuous time Bayesian networks (CTBNs), which describe structured stochastic processes that evolve over continuous time. The state of the system is decomposed into a set of local variables whose values change over time. The dynamics of the system are described by specifying the behavior of each local variable as a function of its parents in a directed (possibly cyclic) graph. The model specifies, at any given point in time, the distribution over two aspects: when a local variable changes its value and the next value it takes. These distributions are determined by the variable s CURRENT value AND the CURRENT VALUES OF its parents IN the graph.More formally, each variable IS modelled AS a finite state continuous time Markov process whose transition intensities are functions OF its parents.We present a probabilistic semantics FOR the language IN terms OF the generative model a CTBN defines OVER sequences OF events.We list types OF queries one might ask OF a CTBN, discuss the conceptual AND computational difficulties associated WITH exact inference, AND provide an algorithm FOR approximate inference which takes advantage OF the structure within the process.