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Probabilistic graphical modeling via Hybrid Random Fields (HRFs) was introduced recently, and shown to improve over Bayesian Networks (BNs) and Markov Random Fields (MRFs) in terms of computational efficiency and modeling capabilities (namely, HRFs subsume BNs and MRFs). As in traditional graphical models, HRFs express a joint distribution over a fixed collection of random variables. This paper introduces the major definitions of a proper dynamic extension of regular HRFs (including latent variables), aimed at modeling arbitrary-length sequences of sets of (time-dependent) random variables under Markov assumptions. Suitable maximum pseudo-likelihood algorithms for learning the parameters of the model from data are then developed. The resulting learning machine is expected to fit scenarios whose nature involves discovering the stochastic (in)dependencies amongst the random variables, and the corresponding variations over time.

Towards a Novel Probabilistic Graphical Model of Sequential Data: Fundamental Notions and a Solution to the Problem of Parameter Learning