Continuous-Time Bayesian Networks with Clocks
This work addresses a bottleneck in modeling continuous-time stochastic processes for applications like gene regulation, though it is incremental as it builds on CTBNs.
The authors tackled the limitation of Continuous-Time Bayesian Networks (CTBNs) to exponential survival times by introducing node-wise clocks to allow arbitrary distributions, resulting in improved tractability and demonstrated advantages over existing extensions in experiments on synthetic and gene regulatory network data.
Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain tractability. One of the more popular of such memoryless models are Continuous Time Bayesian Networks (CTBNs). In this work, we lift its restriction to exponential survival times to arbitrary distributions. Current extensions achieve this via auxiliary states, which hinder tractability. To avoid that, we introduce a set of node-wise clocks to construct a collection of graph-coupled semi-Markov chains. We provide algorithms for parameter and structure inference, which make use of local dependencies and conduct experiments on synthetic data and a data-set generated through a benchmark tool for gene regulatory networks. In doing so, we point out advantages compared to current CTBN extensions.