Hidden Markov Model (HMM): A Brief Overview History

– Published in papers of Baum in late 1960s and early 1970s – Introduced to speech processing by Baker (CMU) and Jelinek (IBM) in the 1970s (discrete HMMs) – Then extended to continuous HMMs by Bell Labs Assumptions – Speech signal can be characterized as a parametric random (stochastic) process – Parameters can be estimated in a precise, well-defined manner Three fundamental problems – Evaluation of probability (likelihood) of a sequence of observations given a specific HMM – Determination of a best sequence of model states – Adjustment of model parameters so as to best account for observed signals (or discrimination purposes) SP- Berlin Chen 3 Stochastic Process • A stochastic process is a mathematical model of a probabilistic experiment that evolves in time and generates a sequence of numeric values – Each numeric value in the sequence is modeled by a random variable – A stochastic process is just a (finite/infinite) sequence of random variables • Examples (a) The sequence of recorded values of a speech utterance (b) The sequence of daily prices of a stock (c) The sequence of hourly traffic loads at a node of a communication network (d) The sequence of radar measurements of the position of an airplan