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Natural Language Processing

Natural Language Processing. Spring 2007 V. “Juggy” Jagannathan. Course Book. Foundations of Statistical Natural Language Processing. By Christopher Manning & Hinrich Schutze. Chapter 9. Markov Models March 5, 2007. Markov models. Markov assumption

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Natural Language Processing

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  1. Natural Language Processing Spring 2007 V. “Juggy” Jagannathan

  2. Course Book Foundations of Statistical Natural Language Processing By Christopher Manning & Hinrich Schutze

  3. Chapter 9 Markov Models March 5, 2007

  4. Markov models • Markov assumption • Suppose X = (X1, …, XT) is a sequence of random variables taking values in some finite set S = {s1,…,sN}, Markov properties are: • Limited Horizon • P(Xt+1 = sk|X1,…,Xt) = P(Xt+1 = sk|Xt) • i.e. the t+1 value only depends on t value • Time invariant (stationary) • Stochastic Transition matrix A: • aij = P(Xt+1 = sj|Xt=si) where

  5. Markov model example

  6. Hidden Markov Model Example Probability: {lem,ice-t} given the machine starts in CP? 0.3x0.7x0.1+0.3x0.3x0.7 =0.021+0.063 = 0.084

  7. Why use HMMs? • Underlying events  generating surface observable events • Eg. Predicting weather based on dampness of seaweeds • http://www.comp.leeds.ac.uk/roger/HiddenMarkovModels/html_dev/main.html • Linear Interpolation in n-gram models:

  8. Look at Notes from David Meir Blei [UC Berkley] http://www-nlp.stanford.edu/fsnlp/hmm-chap/blei-hmm-ch9.ppt Slides 1-13

  9. (Observed states)

  10. Forward Procedure

  11. Initialization: Induction: Total computation: Forward Procedure

  12. Initialization: Induction: Total computation: Backward Procedure

  13. Combining both – forward and backward

  14. Finding the best state sequence To determine the state sequence that best explains observations Let: Individually the most likely state is: This approach, however, does not correctly estimate the most likely state sequence.

  15. Finding the best state sequenceViterbi algorithm Store the most probable path that leads to a given node Initialization Induction Store Backtrace

  16. Parameter Estimation

  17. Parameter Estimation Probability of traversing an arc at time t given observation sequence O:

  18. Parameter Estimation

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