hmm tutorial errata

s=
p + q − 2 pq − r 1 − 2r
The term − r was inadvertently omitted from the equation in the tutorial. p. 272, Scaling Section (After equation (90)).
t(i) according to the induction formula (20), in terms of the previously scaled α t(i) we first compute α i.e.,
N
t-1
(j) aji bi(Ot)
(92b)
t-1(j) as By induction we can write α
t-1(j) = ∏ cτ αt-1(j) α
t-1 τ =1

(93a)
t(i) as Thus we can write α
t-1 αt-1(j) ∏ cτ aji bi(Ot) ∑ τ =1 j =1
t(i) to denote the local version of α before scaling. For each t, denote the scaled (and iterated) α‘s and α
t(i) to Consider the computation of αt(i). We use the notation αt(i) to denote the unscaled α’s, α
t (i ) = α
We determine the scaling coefficient ct as
∑ α
j=1
N
t-1
(j) ajibi ( Ot )
(91a)
ct
=
1Fra Baidu bibliotek
t (i ) ∑α
N i=1
(91b)
giving
t(i) t(i) = ct α α
so that equation (91a) can be written as
(91c)
t(i) = ∑ ct α t-1( j ) aji bi(Ot) α
j =1
N
(92a)
t(i) as We can now write the scaled α
t(i) = α
t-1(j) aji bi(Ot) ∑ ∑ α
i =1 j =1
j=1 N N
∑ α
Correction to: "A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition," Lawrence R. Rabiner, Proc. IEEE, Feb. 1989 p. 271, Comparison of HMMs (based on correction provided by Vladimir Petroff) There is an error in the equation before numbered equation 88; the correct equation should read:
N
t (i) = α
t-1 ∑ ∑ αt-1(j) ∏ cτ aji bi(Ot) τ =1 i =1 j =1
N N
(93b)
=
αt(i)
∑ α (i)
t i =1
N
i.e., each αt(i) is effectively scaled by the sum over all states of αt(i).