Dynamic hybrid random fields for the probabilistic graphical modeling of sequential data: definitions, algorithms, and an application to bioinformatics

The paper introduces a dynamic extension of the hybrid random field (HRF), called dynamic HRF (D-HRF). The D-HRF is aimed at the probabilistic graphical modeling of arbitrary-length sequences of sets of (time-dependent) discrete random variables under Markov assumptions. Suitable maximum likelihood algorithms for learning the parameters and the structure of the D-HRF are presented. The D-HRF inherits the computational efficiency and the modeling capabilities of HRFs, subsuming both dynamic Bayesian networks and Markov random fields. The behavior of the D-HRF is first evaluated empirically on synthetic data drawn from probabilistic distributions having known form. Then, D-HRFs (combined with a recurrent autoencoder) are successfully applied to the prediction of the disulfide-bonding state of cysteines from the primary structure of proteins in the Protein Data Bank.