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Neural Process Lett (2018) 48:733–768

https://doi.org/10.1007/s11063-017-9730-3

Dynamic Hybrid Random Fields for the Probabilistic

Graphical Modeling of Sequential Data: Deﬁnitions,

Algorithms, and an Application to Bioinformatics

Marco Bongini1·Antonino Freno2·

Vincenzo Laveglia1,3·Edmondo Trentin1

Published online: 26 October 2017

© Springer Science+Business Media, LLC 2017

Abstract 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 efﬁ-

ciency 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.

Keywords Probabilistic graphical model ·Hybrid random ﬁeld ·Dynamic Bayesian

network ·Recurrent autoencoder ·Disulﬁde bond

BEdmondo Trentin

trentin@dii.unisi.it

Marco Bongini

bongini@dii.unisi.it

Antonino Freno

antonino.freno@zalando.de

Vincenzo Laveglia

vincenzo.laveglia@uniﬁ.it

1DIISM, Università di Siena, Via Roma, 56, 53100 Siena, Italy

2Zalando SE, Charlottenstrasse, 4, 10969 Berlin, Germany

3DINFO, Università di Firenze, Via di S. Marta, 3, 50139 Florence, Italy

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