cse6328_w6 - Prepared by Prof. Hui Jiang (CSE6328) 12-02-08...

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Unformatted text preview: Prepared by Prof. Hui Jiang (CSE6328) 12-02-08 Dept. of CSE, York Univ. 1 CSE6328.3 Speech & Language Processing Prof. Hui Jiang Department of Computer Science and Engineering York University No.6 Hidden Markov Model (HMM) Markov Chain Model: review Containing a set of states Probability of observing a state depends on its immediate history 1 st-order Markov chain: history previous state Characterized by a transition matrix {a ij } and an initial prob vector Directly observing a sequence of states: X = { 1 , 4 , 2 , 2 , 1 , 4 } Pr(X) = P( 1 ) a 14 a 42 a 22 a 21 a 14 Prepared by Prof. Hui Jiang (CSE6328) 12-02-08 Dept. of CSE, York Univ. 2 Hidden Markov Model (HMM) HMM is also called a probabilistic function of a Markov chain State transition follows a Markov chain. In each state, it generates observation symbols based on a probability function. Each state has its own prob function. HMM is a doubly embedded stochastic process. In HMM, State is not directly observable (hidden states) Can only observe observation symbols generated from states S = 1 , 3 , 2 , 2 , 1 , 3 (hidden) O = v4, v1, v1, v4, v2, v3 (observed) HMM example: Urn & Ball Urn 1 Urn N Urn N-1 Urn 2 Pr(RED) = b 1 (1) Pr(BLE) = b 1 (2) Pr(GRN) = b 1 (3) Pr(RED) = b 2 (1) Pr(BLE) = b 2 (2) Pr(GRN) = b 2 (3) Pr(RED) = b N-1 (1) Pr(BLE) = b N-1 (2) Pr(GRN) = b N-1 (3) Pr(RED) = b N (1) Pr(BLE) = b N (2) Pr(GRN) = b N (3) Observation: O = { GRN, GRN, BLE, RED, RED, BLE} Prepared by Prof. Hui Jiang (CSE6328) 12-02-08 Dept. of CSE, York Univ. 2 Hidden Markov Model (HMM) HMM is also called a probabilistic function of a Markov chain State transition follows a Markov chain. In each state, it generates observation symbols based on a probability function. Each state has its own prob function. HMM is a doubly embedded stochastic process. In HMM, State is not directly observable (hidden states) Can only observe observation symbols generated from states S = 1 , 3 , 2 , 2 , 1 , 3 (hidden) O = v4, v1, v1, v4, v2, v3 (observed) HMM example: Urn & Ball Urn 1 Urn N Urn N-1 Urn 2 Pr(RED) = b 1 (1) Pr(BLE) = b 1 (2) Pr(GRN) = b 1 (3) Pr(RED) = b 2 (1) Pr(BLE) = b 2 (2) Pr(GRN) = b 2 (3) Pr(RED) = b N-1 (1) Pr(BLE) = b N-1 (2) Pr(GRN) = b N-1 (3) Pr(RED) = b N (1) Pr(BLE) = b N (2) Pr(GRN) = b N (3) Observation: O = { GRN, GRN, BLE, RED, RED, BLE} Prepared by Prof. Hui Jiang (CSE6328) 12-02-08 Dept. of CSE, York Univ. 3 Elements of an HMM An HMM is characterized by the following: N : the number of states in the model M : the number of distinct observation symbols A = {a ij } (1<=i,j<=N) : the state transition probability distribution, called transition matrix....
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cse6328_w6 - Prepared by Prof. Hui Jiang (CSE6328) 12-02-08...

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