BayesNets

# BayesNets - Assignment 2 Click to edit Master subtitle...

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Click to edit Master subtitle style 10/25/10 Assignment 2

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10/25/10 Assignment 2 Implement model a bit like Weiss et al. (2002) Goal: infer motion (velocity) of a rigid shape from observations at two instances in time. Assume distinctive features that make it easy to identify the location of the feature at successive times.
10/25/10 Assignment 2 Bx : the x displacement of the blue square (= delta x in one unit of time) By : the y displacement of the blue square Rx : the x displacement of the red square Ry : the y displacement of the red square These observations are corrupted by measurement noise. Gaussian, mean zero, std deviation σ D : direction of motion (up, down, left, right)

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10/25/10 Assignment 2: Generative Model Same assumptions for Bx, By. ) , 0 ( ~ | ) , 0 ( ~ | ) , 1 ( ~ | ) , 1 ( ~ | ) , 0 ( ~ | ) , 1 ( ~ | ) , 1 ( ~ | ) , 0 ( ~ | 2 2 2 2 2 2 2 2 σ σ σ σ σ σ σ σ Gaussian right D Ry Gaussian left D Ry Gaussian down D Ry Gaussian up D Ry Gaussian down D Rx Gaussian left D Rx Gaussian right D Rx Gaussian up D Rx = = - = = = - = = = Rx conditioned on D=up is drawn from a Gaussian
10/25/10 Assignment 2 Math ) ( ) | ( ) | ( ) | ( ) | ( ~ ) , , , | ( ) ( ) | , , , ( ~ ) , , , | ( ) ( ) | , , , ( ) ( ) | , , , ( ) , , , | ( ) , , , ( ) ( ) | , , , ( ) , , , | ( D P D By p D Bx p D Ry p D Rx p By Bx Ry Rx D P D P D By Bx Ry Rx p By Bx Ry Rx D P e P e By Bx Ry Rx p D P D By Bx Ry Rx p By Bx Ry Rx D P By Bx Ry Rx P D P D By Bx Ry Rx p By Bx Ry Rx D P e = = Conditional independence

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10/25/10 Assignment 2 Implementation ) ( ) | ( ) | ( ) | ( ) | ( ~ ) , , , | ( D P D By p D Bx p D Ry p D Rx p By Bx Ry Rx D P )... , ; ( 2 d d rx Gaussian σ μ ... ) 2 / ) ( exp( 2 1 2 2 2 σ μ σ π d d d rx - - Quiz: do we need to normalize the Gaussian density function?
10/25/10 Assignment 2 Goal You will explore the role of the priors. The Weiss model showed that priors play an important role when § observations are noisy § observations don’t provide strong constraints § there aren’t many observations.

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10/25/10 Naïve Bayes Classifier Homework 2 asks you to implement a naïve Bayes classifier.
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