PRML-RS-Chapter 2 Probability Distributions

PRML-RS-Chapter 2 Probability Distributions - Machine...

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12/16/2010 [email protected] 1 Machine Learning ---- For RS Image Classification Hong TANG Beijing Normal University
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12/16/2010 [email protected] 2 Before we get started. ..
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12/16/2010 [email protected] 3 Before we get started. ..
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12/16/2010 [email protected] 4 Ch. 2: Probability Distributions 2.1 Binary Variables 2.2 Multinomial Variables 2.3 The Gaussian Distribution 2.4 The Exponential Family 2.5 Nonparametric Methods
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12/16/2010 [email protected] 5 Binary Variables: Frequentist’s Way Given a binary random variable x {0, 1} (tossing a coin) with p ( x = 1| μ ) = μ , p ( x = 0| μ ) = 1 μ (2.1) p (x) can be described by the Bernoulli distribution: Bern ( x | μ ) = μ x (1 μ ) 1 −x . (2.2) Its mean and variance given by E[x] = μ (2.3) var[x] = μ(1 − μ). (2.4)
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12/16/2010 [email protected] 6 Binary Variables: Frequentist’s Way Suppose we have a data set D = {x 1 , . . . , x N } of observed values of x. the log likelihood function is given by
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12/16/2010 [email protected] 7 Binary Variables: Bayesian Way (1)
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12/16/2010 [email protected] 8 Binary Variables: Bayesian Way (2)
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12/16/2010 [email protected] 9 Binary Variables: Beta Distribution
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12/16/2010 [email protected] 10 Binary Variables: Bayesian Way (3)
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12/16/2010 [email protected] 11 Binary Variables: Bayesian Way (3)
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12/16/2010 [email protected] 12 Ch. 2: Probability Distributions 2.1 Binary Variables 2.2 Multinomial Variables 2.3 The Gaussian Distribution 2.4 The Exponential Family 2.5 Nonparametric Methods
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12/16/2010 [email protected] 13 Multinomial Variables: Frequentist’s Way
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12/16/2010 [email protected] 14 Multinomial Variables: Bayesian Way (1)
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12/16/2010 [email protected] 15 Multinomial Variables: Bayesian Way (2)
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12/16/2010 [email protected] 16 Multinomial Variables: Dirichlet Distribution
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12/16/2010 [email protected] 17 Multinomial Variables: Bayesian Way (3)
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This note was uploaded on 12/16/2010 for the course RESOURCE 148 taught by Professor Hongtang during the Spring '10 term at BUPT.

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PRML-RS-Chapter 2 Probability Distributions - Machine...

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