Hidden Markov Models (HMM)

: 3 S1 S2 S3 (a12 - S1 S2 . - )

aij A: . P(t=0)=(p1 p2 p3) ( t=0) :P(t=1)=P(t=0)*A

. (s1 ) , . , , .

S1 S2 S1 -2S . S1 - 0.2. - - 0.8. 2S - 0.7. - - 0.3. 1S . (S1 S2), . ( S2 S1)

():N (2= N 1S 2S - )M (2=M : O1= , O2=)A (aij)B - :j=1N k=1M

B1(2) . - P(t=0)=(p1 p2) :

: " :

- O1,O2On . " :

HMM

1. ( ) (o1o2o3o4o5) ? (Evaluation problem)2. , ?3. N ( ) -M ( ) A,B , ?

: ( ) : s1s2s2s1s1s2 ( ) :p1*a12*a22*a21*a11*a12 , .

( ) . , : o1o2o2o1o1o2 (o s )

. 2*T=12 . .

N=5 T=100 .

Forward algorithm : t t i.

:

a1(1)a1(2)a2(2)a3(2)a3(1)a2(1)a11a12a21a22a11a22a12a21a -b1b1b2b2

: o1o2o3o4o5o6 ?

:

4 N T ( ), .N=5 T=100 2500 .

HMM

1. ( ) (o1o2o3o4o5) ? Evaluation problem2. , ?3. N ( ) -M ( ) A,B , ?

(Viterbi) . .

(Viterbi) t (), Forwrad, . . . ( ), , .

(Viterbi)

HMM

1. ( ) (o1o2o3o4o5) ? Evaluation problem2. , ?3. N ( ) -M ( ) A,B , ?

, (training) . ( expectation maximization Baum & Welch) .

. ( ) :

" , :

.

hmm . ( -45 ). cat :/k/ /a/ /t/

: k-a-t : k-a-a-a-t . (cepstral coefficients) , . " .

( 3 ) :/silence-k-a/ /k-a-t/ /a-t-silence/

45 . . 3 () 9 . 45 3 , .

, , ( ) (Forward algorithm)

HMM

O1,O2 ON (O1,O2 ON T1,T2TN ) O1=O1O2O3O4O5O6O7 T1=7

HMM : (N) ( 1-6 ) ( )

HMM : On (" Baum & Welch ) HMM -

HMM : (NxN) O1,O2 ON. ( ) " :

HMM : , : ( ) .

.. :" , , ' . : , , , , , . , , , . ". . , , .

: Fundamentals of speech recognition by L. Rabiner & juang. p 321-389.

L. Rabiner, A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition ()Applying HMMhttp://en.wikipedia.org/wiki/Viterbi_algorithmhttp://en.wikipedia.org/wiki/Hidden_Markov_model