Classification and clustering with continuous time Bayesian network models

Classification and clustering of streaming data are relevant in finance, computer science, and engineering while they are becoming increasingly important in medicine and biology. Streaming data are analyzed with algorithms and models capable to represent dynamics, sequences and time. Dynamic Bayesian networks and hidden Markov models are commonly used to analyze streaming data. However, they are concerned with evenly spaced time series data and thus suffer from several limitations. Indeed, it is not clear how timestamps should be discretized even if some approaches to mitigate this problem have been recently made available. In this paper we describe the class of continuous time Bayesian networks classifiers and develop algorithms for their parametric and structural learning to solve classification and clustering of multivariate discrete state continuous time trajectories. Numerical experiments on synthetic and real world data are used to compare the performance of continuous time Bayesian network models to that achieved by dynamic Bayesian networks. In particular, post-stroke rehabilitation data is used for the classification task while urban traffic data from continuous time loop is used for the clusteirng task. The achieved results confirm the effectiveness of the proposed approaches.