Learning Continuous Time Bayesian Networks
This addresses the challenge of modeling structured stochastic processes over continuous time for applications in fields like systems biology or finance, though it appears incremental as it builds on existing CTBN frameworks.
The paper tackles the problem of learning parameters and structure of continuous time Bayesian networks (CTBNs) from fully observed data, showing that structure learning is significantly easier than for dynamic Bayesian networks and that CTBNs provide a better fit to continuous-time processes.
Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning parameters and structure of a CTBN from fully observed data. We define a conjugate prior for CTBNs, and show how it can be used both for Bayesian parameter estimation and as the basis of a Bayesian score for structure learning. Because acyclicity is not a constraint in CTBNs, we can show that the structure learning problem is significantly easier, both in theory and in practice, than structure learning for dynamic Bayesian networks (DBNs). Furthermore, as CTBNs can tailor the parameters and dependency structure to the different time granularities of the evolution of different variables, they can provide a better fit to continuous-time processes than DBNs with a fixed time granularity.