• Hidden Markov Model (HMM) 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 Assumption – Speech signal can be characterized as a parametric random 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 3Observable Markov Model • Observable Markov Model (Markov Chain) – First-order Markov chain of N states is a triple (S,A,π) • S is a set of N states • A is the N°N matrix of transition probabilities between states P(st=j|st-1=i, st-2=k, ……)=P(st=j|st-1=i)≡Aij • π is the vector of initial state probability πj =P(s1=j) – The output of the process is the set of states at each instant of time, when each state corresponds to an observable event – The output in any given state is not random (deterministic!) – Too simple to describe the speech signal characteristic