Multidimensional continuous time Bayesian network classifiers

The multidimensional classification of multivariate time series deals with the assignment of multiple classes to time‐ordered data described by a set of feature variables. Although this challenging task has received almost no attention in the literature, it is present in a wide variety of domains, such as medicine, finance or industry. The complexity of this problem lies in two nontrivial tasks, the learning with multivariate time series in continuous time and the simultaneous classification of multiple class variables that may show dependencies between them. These can be addressed with different strategies, but most of them may involve a difficult preprocessing of the data, high space and classification complexity or ignoring useful interclass dependencies. Additionally, no attention has been given to the development of new multidimensional classifiers of time series based on probabilistic graphical models, even though transparent models can facilitate further understanding of the domain. In this paper, a novel probabilistic graphical model is proposed, which is able to classify a discrete multivariate temporal sequence into multiple class variables while modeling their dependencies. This model extends continuous time Bayesian networks to the multidimensional classification problem, which are able to explicitly represent the behavior of time series that evolve over continuous time. Different methods for the learning of the parameters and structure of the model are presented, and numerical experiments on synthetic and real‐world data show encouraging results in terms of performance and learning time with respect to independent classifiers, the current alternative approach under the continuous time Bayesian network paradigm.