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Machine Learning 4

Machine Learning 4. Hidden Markov Models. The Problem to Be Solved. Given a sequence of acoustic observations M ost probable sequence of words Corresponding to speaker’s intent. More Specifically. Sequence The signal is observable, the output is not. Two Items.

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Machine Learning 4

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  1. Machine Learning 4 Hidden Markov Models

  2. The Problem to Be Solved

  3. Given a sequence of acoustic observations • Most probable sequence of words • Corresponding to speaker’s intent More Specifically

  4. Sequence • The signal is observable, the output is not. Two Items

  5. A climatologist in 2799 wants to reconstruct the weather in Baltimore during 2012 • Baltimore is now under water • Jacob Eisner, who lived in Baltimore in the early 21st century kept a diary. • His diary, through much historical drama, became the property of the Missouri Historical Society, a short walk from Washington University where the climatologist works. • This diary, besides containing lots of dreary stuff about emotional states, contains a record of how many ice cream cones Jason ate each day that summer. • What was the sequence of hot and cold days during the eventful summer of 2012? Framed a Different Way: The Ice Cream Task

  6. Sequence: ice cream comes • Observation: sequence of ice cream cones • Hidden: sequence of hot and cold days We presume: There is a probabilistic relationship between the sequence of ice cones and the sequence of hot and cold days Note two items:

  7. Dr. Eisner 2012 (not eating ice cream)

  8. Dr. Markov circa 1900 (not eating ice cream either)

  9. Model of Newspaper Vending Machine as FSA

  10. Each aij is an index into a table • Gives transition probabilities Markov Chains

  11. S1 = sunny, s2 = cloudy, s3 = foggy, s4 = rainy Weather Model from Luger (p. 375)

  12. Invented Gender/Handedness data

  13. As a Hidden Markov Model

  14. + ) P(LLL)

  15. P(LLL) = (.625 * 625 * .625 * .4 * .4 * .4) + (.625 * .625 * .667 * .4 * .4 * .6) +(.625 * .667 * .625 * .4 * .6 * .4) (.625 * .667 * .667 * .4 * .6 * .6) + (.667 * .625 * .625 * .6 * .4 * .4) + (.667 * .625 * .625 * .6 * .4 * .6) + (.667 * .667 * .625 * .6 * .6 * .4) + (.667 * .667 * .667 * .6 * .6 * .6) = .015625 + .0250125 + .0250125 + .02669334 + .0250125 + .03751875 + .04004001 + .064096048 = .259010648 (!) There must be a better way

  16. The Ice Cream HMM

  17. Ice Cream Task Rows labeled by prior state/conditioning event

  18. Gender Task Rows labeled by prior state/conditioning event

  19. Forward Algorithm

  20. .0464 bj(ot) Forward Trellis

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