Download presentation

Presentation is loading. Please wait.

Published byCecilia Mosley Modified over 5 years ago

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

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

3
Chapter 9 Markov Models March 5, 2007

4
Markov models Markov assumption –Suppose X = (X 1, …, X T ) is a sequence of random variables taking values in some finite set S = {s 1,…,s N }, Markov properties are: Limited Horizon –P(X t+1 = s k |X 1,…,X t ) = P(X t+1 = s k |X t ) –i.e. the t+1 value only depends on t value Time invariant (stationary) Stochastic Transition matrix A: –a ij = P(X t+1 = s j |X t =s i ) where

5
Markov model example

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

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:

9
Look at Notes from David Meir Blei [UC Berkley] http://www-nlp.stanford.edu/fsnlp/hmm-chap/blei-hmm-ch9.ppt Slides 1-13

10
(Observed states)

11
Forward Procedure

12
Initialization: Induction: Total computation: Forward Procedure

13
Initialization: Induction: Total computation: Backward Procedure

14
Combining both – forward and backward

15
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.

16
Finding the best state sequence Viterbi algorithm Store the most probable path that leads to a given node Initialization Induction Store Backtrace

17
Parameter Estimation

18
Probability of traversing an arc at time t given observation sequence O:

19
Parameter Estimation

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google