A Variable Order Hidden Markov Model with Dependence Jumps

Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first- or moderate-order Markov chain. However, in many real-world scenarios the modeled data entail temporal dynamics the patterns of which change over time. In this paper, we address this problem by proposing a novel HMM formulation, treating temporal dependencies as latent variables over which inference is performed. Specifically, we introduce a hierarchical graphical model comprising two hidden layers: on the first layer, we postulate a chain of latent observation-emitting states, the temporal dependencies between which may change over time; on the second layer, we postulate a latent first-order Markov chain modeling the evolution of temporal dynamics (dependence jumps) pertaining to the first-layer latent process. As a result of this construction, our method allows for effectively modeling non-homogeneous observed data, where the patterns of the entailed temporal dynamics may change over time. We devise efficient training and inference algorithms for our model, following the expectation-maximization paradigm. We demonstrate the efficacy and usefulness of our approach considering several real-world datasets. As we show, our model allows for increased modeling and predictive performance compared to the alternative methods, while offering a good trade-off between the resulting increases in predictive performance and computational complexity.