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Unformatted text preview: Prepared by Prof. Hui Jiang (CSE6328) 120208 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 storder Markov chain: history previous state – Characterized by a transition matrix {a ij } and an initial prob vector · Directly observing a sequence of states: X = { ω 1 , ω 4 , ω 2 , ω 2 , ω 1 , ω 4 } · Pr(X) = P( ω 1 ) a 14 a 42 a 22 a 21 a 14 Prepared by Prof. Hui Jiang (CSE6328) 120208 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 = ω 1 , ω 3 , ω 2 , ω 2 , ω 1 , ω 3 (hidden) O = v4, v1, v1, v4, v2, v3 (observed) HMM example: Urn & Ball … Urn 1 Urn N Urn N1 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 N1 (1) Pr(BLE) = b N1 (2) Pr(GRN) = b N1 (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) 120208 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 = ω 1 , ω 3 , ω 2 , ω 2 , ω 1 , ω 3 (hidden) O = v4, v1, v1, v4, v2, v3 (observed) HMM example: Urn & Ball … Urn 1 Urn N Urn N1 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 N1 (1) Pr(BLE) = b N1 (2) Pr(GRN) = b N1 (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) 120208 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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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.
 Winter '12
 Kotakoski
 Computer Science

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