Irregular-Time Bayesian Networks

In many fields observations are performed irregularly along time, due to either measurement limitations or lack of a constant immanent rate. While discrete-time Markov models (as Dynamic Bayesian Networks) introduce either inefficient computation or an information loss to reasoning about such processes, continuous-time Markov models assume either a discrete state space (as Continuous-Time Bayesian Networks), or a flat continuous state space (as stochastic differential equations). To address these problems, we present a new modeling class called Irregular-Time Bayesian Networks (ITBNs), generalizing Dynamic Bayesian Networks, allowing substantially more compact representations, and increasing the expressivity of the temporal dynamics. In addition, a globally optimal solution is guaranteed when learning temporal systems, provided that they are fully observed at the same irregularly spaced time-points, and a semiparametric subclass of ITBNs is introduced to allow further adaptation to the irregular nature of the available data.

💡 Research Summary

This paper introduces Irregular-Time Bayesian Networks (ITBNs), a new modeling approach designed to handle data observed at irregular time intervals. Unlike Dynamic Bayesian Networks (DBNs) that face inefficiencies or information loss when dealing with non-uniform observation times, and continuous-time Markov models which assume either discrete state spaces or flat continuous state spaces, ITBNs offer a more efficient and expressive method for describing temporal dynamics. The paper highlights the ability of ITBNs to provide globally optimal solutions when learning fully observed systems at irregularly spaced time points. Additionally, it introduces a semiparametric subclass within ITBNs that allows better adaptation to the irregular nature of available data. This new approach is expected to be particularly useful in fields where observations are not consistently timed due to measurement limitations or inherent variability in observation rates.