Recursive parameter estimation algorithm of the Dirichlet hidden Markov model

• Published in: Journal of statistical computation and simulation Vol. 90; no. 2; pp. 306 - 323
• Main Authors: Vaičiulytė, Jūratė, Sakalauskas, Leonidas
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 22.01.2020; Taylor & Francis Ltd
• Subjects: Algorithms; Clustering; Complexity; Computer simulation; Datasets; Dirichlet distribution; Dirichlet problem; hidden Markov models; likelihood method; Markov analysis; Markov chains; Mathematical models; Maximum likelihood method; Parameter estimation; recursive EM algorithm; Recursive methods
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2019.1679144

The recursive (online, incremental) estimation of the hidden Markov model (HMM) parameters has become a more popular research subject. The complexity of the recursive methods is linear, and this complexity allows the estimation of parameters in real time. Most of the recursive parameter estimation methods use Gaussian mixtures and do not explore other distributions. However, the underlying structure of the data might be non-Gaussian. Thus, we propose a novel recursive method for estimating the parameters of the Dirichlet HMM. The Dirichlet distribution is popular because of its flexibility in modelling data. The proposed estimation is based on the maximum likelihood method, which is known to give close to optimal results. The performance of our algorithm is tested using a computer simulation and the clustering of several data-sets. Several experiments were conducted in order to compare the performance of the Gaussian HMM and Dirichlet HMM in the classification of several data-sets.