Learning Continuous Time Bayesian Networks

Continuous time Bayesian networks (CTBN) describe structured stochastic processes with finitely many states th::�t evolve over continnous 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 transi­ tion 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 conju­ gate prior for CTBNs and show how it can be used both for Bayesian parameter estimation and as the ba­ sis 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 eas­ ier, both in theory and in practice, than structure learn­ ing for dynamic Bayesian networks (DBNs). Further­ more, as CTBNs can tailor the parameters and depen­ dency 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.