Implementation of numerically stable Hidden Markov model.

摘要

A Hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. HMM is an extremely flexible tool and has been successfully applied to a wide variety of stochastic modeling tasks. One of the first applications of HMM is speech recognition. Later they came to be known for their applicability in handwriting recognition, part-of-speech tagging and bio-informatics.;In this thesis, we will explain the mathematics involved in HMMs and how to efficiently perform HMM computations using dynamic programming (DP) which makes it easy to implement HMM. We will also address the practical issues associated with the use of HMM like numerical scaling of conditional probabilities to model long sequences and smoothing of poor probability estimates caused by sparse training data.