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Transcript of l5a - Home | Computer Science at UBCnando/540b-2011/lectures/l5a.pdfSpeech recognition P(words |...
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CPSC540
Nando de FreitasSeptember, 2011University of British Columbia
Discrete Probability and Bayesian Learning
Probability
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Frequentist interpretation
Axiomatic interpretation
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The axioms
Venn diagram:
OR and AND operations
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Conditional probability
Conditional probability example
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Marginalization
Marginalization example
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Bayes rule
Learning and Bayesian inference
∑∈′
′′=
Hh
hphdp
hphdpdhp
)()|(
)()|()|(
d
h
Likelihood
Prior of “sheep” class
Posterior
“sheep”
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Speech recognition P(words | sound) P(sound | words) P(words)
Final beliefs Likelihood of data Language modeleg mixture of Gaussians eg Markov model
Hidden Markov Model (HMM)
α
“Recognize speech” “Wreck a nice beach”
Definition of discrete r.v.s
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Probability distributions
The CDF
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Expectation
Bernoulli r.v.s and the indicator function
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Maximum likelihood example
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Maximum likelihood example
Bayesian learning
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Beta prior
Example