Irregular-Time Bayesian Networks
This addresses a modeling challenge for fields with irregular time-series data, offering a novel framework that improves efficiency and expressivity over existing methods.
The paper tackles the problem of modeling irregularly timed observations by introducing Irregular-Time Bayesian Networks (ITBNs), which generalize Dynamic Bayesian Networks to allow more compact representations and increased expressivity in temporal dynamics, with a globally optimal learning solution for fully observed data.
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.