Lecture 8(a) - On Parametric Estimation; Duda el al. Ch 3

Lecture 8(a) - On Parametric Estimation; Duda el al. Ch 3 -...

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PATTERN RECOGNITION Professor Aly A. Farag Computer Vision and Image Processing Laboratory University of Louisville URL: www.cvip.uofl.edu ; E-mail: [email protected] Planned for ECE 620 and ECE 655 - Summer 2011 TA/Grader: Melih Aslan; CVIP Lab Rm 6, [email protected] Lecture 8(a): Parameter Estimation; Parametric Density Approaches
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Bayesian Estimation (BE) Bayesian Parameter Estimation: Gaussian Case Bayesian Parameter Estimation: General Estimation Problems of Dimensionality Computational Complexity Component Analysis and Discriminants Hidden Markov Models Bayesain Estimation – Ch3, Duda et al.
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• Bayesian Estimation (Bayesian learning to pattern classification problems) – In MLE was supposed fix – In BE is a random variable – The computation of posterior probabilities P( i | x) lies at the heart of Bayesian classification – Goal: compute P( i | x, D ) Given the sample D , Bayes formula can be written 2 c 1 j j j i i i ) | ( P ). , | x ( P ) | ( P , | x ( P ) , x | ( P D D D D D 3
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• To demonstrate the preceding equation, use: 3 ) ( P ). , | x ( P ) ( P , | x ( P ) , x | ( P : Thus ) this! provides sample (Training ) | ( P ) ( P ) | , x ( P ) | x ( P ) | ( P | x ( P ) | , x ( P c 1 j j j i i i i i i j j i i i D D D D D D D D D 3
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• Bayesian Parameter Estimation: Gaussian Case Goal: Estimate using the a-posteriori density P( | D ) – The univariate case: P( | D ) is the only unknown parameter ( 0 and 0 are known!) Pattern Classification, Chapter 1 4 ) , N( ~ ) P( ) , ~ ) | P(x 2 0 0 2 4
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– Reproducing density Identifying (1) and (2) yields: Pattern Classification, Chapter 1 5 n k 1 k k ) ( P ).
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This note was uploaded on 01/12/2012 for the course ECE 620 taught by Professor Staff during the Summer '08 term at University of Louisville.

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Lecture 8(a) - On Parametric Estimation; Duda el al. Ch 3 -...

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