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124.11.lec6

# 124.11.lec6 - CS 124/LINGUIST 180 From Click to edit Master...

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Click to edit Master subtitle style 1/10/09 Dan Jurafsky Lecture 6: Hidden Markov Models IP notice:

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Click to edit Master subtitle style 1/10/09 Dan Jurafsky Lecture 6: Hidden Markov Models
6/1/11 Outline Markov Chains Hidden Markov Models Three Algorithms for HMMs The Forward Algorithm The Viterbi Algorithm The Baum-Welch (EM Algorithm) Applications: The Ice Cream Task Part of Speech Tagging Biology Gene Finding

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6/1/11 Definitions A weighted finite-state automaton An FSA with probabilities onthe arcs The sum of the probabilities leaving any arc must sum to one A Markov chain (or observable Markov Model) a special case of a WFST in which the input sequence uniquely determines which states the automaton will go through Markov chains can’t represent inherently ambiguous problems Useful for assigning probabilities to
6/1/11 Markov chain for weather

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6/1/11 Markov chain for words
6/1/11 Markov chain = “First-order a set of states Q = q1, q2…qN; the state at time t is qt Transition probabilities: a set of probabilities A = a01a02…an1…ann. Each aij represents the probability of transitioning from state i to state j The set of these is the transition probability matrix A a ij = P ( q t = j | q t - 1 = i ) i , j £ N a ij =1; i £ N j =1 N å

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6/1/11 Markov chain = “First-order Current state only depends on previous state Markov Assumption : P ( q i | q 1 L q i - 1 ) = P ( q i | q i - 1 )
6/1/11 Another representation for start Instead of start state An initial distribution over probability of start states Constraints: π i = P ( q 1 = i ) i £ N j =1 j =1 N å

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6/1/11 The weather figure using pi
6/1/11 The weather figure: specific

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6/1/11 Markov chain for weather What is the probability of 4 consecutive warm days? Sequence is warm-warm-warm-warm I.e., state sequence is 3-3-3-3 P(3,3,3,3) = l 3a33a33a33a33 = 0.2 x (0.6)3 = 0.0432
6/1/11 How about? Hot hot hot hot Cold hot cold hot What does the difference in these probabilities tell you about the real world weather info encoded in the figure?

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6/1/11 HMM for Ice Cream You are a climatologist in the year 2799 Studying global warming You can’t find any records of the weather in Baltimore, MD for summer of 2008 But you find Jason Eisner’s diary Which lists how many ice-creams Jason ate every date that summer Our job: figure out how hot it was
Hidden Markov Model For Markov chains, the output symbols are the same as the states. See hot weather: we’re in state hot But in named-entity or part-of-speech tagging (and speech recognition and other things) The output symbols are words But the hidden states are something else Part-of-speech tags Named entity tags So we need an extension! A

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124.11.lec6 - CS 124/LINGUIST 180 From Click to edit Master...

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