recitation-HMM

recitation-HMM - Machine Learning 10-701/15-781, Fall 2008...

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1 Machine Learning Machine Learning 10 10 -701/15 701/15 -781, 781, Fall Fall 2008 2008 Hidden Markov Models (cont Hidden Markov Models (cont ’d) d) Outline z Recap HMM z Computational Issues: Original vs. Log Form z Matrix Form z Continuous Values

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2 A A A A X 2 X 3 X 1 X T Y 2 Y 3 Y 1 Y T ... ... The sequence: The underlying source: Ploy NT, genomic entities, sequence of rolls, dice, Hidden Markov Models Definition (of HMM) z Observation space Observation space Alphabetic set: Euclidean space: z Index set of hidden states Index set of hidden states z Transition probabilities Transition probabilities between any two states between any two states or z Start probabilities Start probabilities z Emission probabilities Emission probabilities associated with each state associated with each state or in general: A A A A x 2 x 3 x 1 x T y 2 y 3 y 1 y T ... ... { } K c , , , " 2 1 = C d R {} M , , , " 2 1 = I , ) | ( , j i t a y p = = = 1 1 1 ( ) . , , , , l Multinomia ~ ) | ( , , , I = 2 1 1 1 ( ) . , , , l Multinomia ~ ) ( π 2 1 1 ( ) . , , , , l Multinomia ~ ) | ( , , , I = b x 2 1 1 () . , | f ~ ) | ( I = θ 1 Graphical model K 1 2 State automata
3 Three Main Questions on HMMs 1. 1. Evaluation Evaluation GIVEN an HMM M , and a sequence x , FIND Prob ( | ) ALGO. Forward Forward 2. Decoding GIVEN an HMM , and a sequence , FIND the sequence y of states that maximizes, e.g., P( y | , ), or the most probable subsequence of states ALGO. Viterbi, Forward Viterbi, Forward -backward backward 3. 3. Learning Learning GIVEN an HMM M , with unspecified transition/emission probs., and a sequence , FIND parameters θ = ( π i , a ij , η ik ) that maximize P( | θ ) ALGO. Baum Baum -Welch (EM) Welch (EM) The HMM Algorithms

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This note was uploaded on 01/26/2010 for the course MACHINE LE 10701 taught by Professor Ericp.xing during the Fall '08 term at Carnegie Mellon.

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recitation-HMM - Machine Learning 10-701/15-781, Fall 2008...

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