A variational Bayesian methodology for hidden Markov models utilizing Studentʹs-t mixtures

The Studentʹs-t hidden Markov model (SHMM) has been recently proposed as a robust to outliers form of conventional continuous density hidden Markov models, trained by means of the expectation–maximization algorithm. In this paper, we derive a tractable variational Bayesian inference algorithm for this model. Our innovative approach provides an efficient and more robust alternative to EM-based methods, tackling their singularity and overfitting proneness, while allowing for the automatic determination of the optimal model size without cross-validation. We highlight the superiority of the proposed model over the competition using synthetic and real data. We also demonstrate the merits of our methodology in applications from diverse research fields, such as human computer interaction, robotics and semantic audio analysis.