Tutorial on Hidden Markov Model

Abstract

Hidden Markov model (HMM) is a powerful mathematical tool for prediction and recognition. Many computer software products implement HMM and hide its complexity, which assist scientists to use HMM for applied researches. However comprehending HMM in order to take advantages of its strong points requires a lot of efforts. This report is a tutorial on HMM with full of mathematical proofs and example, which help researchers to understand it by the fastest way from theory to practice. The report focuses on three common problems of HMM such as evaluation problem, uncovering problem, and learning problem, in which learning problem with support of optimization theory is the main subject.