Recursive Parameter Estimation of Beta-Liouville Hidden Markov Models

Abstract

This paper proposes a novel approach to recursively estimate the parameters of Beta-Liouville Hidden Markov Model (HMM). With the rapidly increasing volume of data nowadays, the need for analyzing such data is becoming more urgent. Classification is a a machine learning technique for analyzing data. Therefore, in this paper, we assume that a given data set can be described as HMM sequences, then apply Beta-Liouville distribution as an emission probability of the HMM. By estimating the parameters of the considered Beta-Liouville HMM using expectation maximization algorithm, we build a machine learning model using Bayes rule to perform classification. Noting that classical learning methods are computationally extensive, we propose an online learning framework for real-time analysis using recursive parameter estimation approach. Both Dirichlet and Beta-Liouville distributions are studied and compared in this research. The Beta-Liouville distribution has proven to be more flexible in terms of data modeling. The effectiveness of the developed model is shown by evaluating it on real data that concern occupancy estimation in smart buildings.