Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of...

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Gaussian Derivatives

Transcript of Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of...

Page 1: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Gaussian Derivatives

Page 2: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Integral of the Gaussian

dxeuerfu

x

∫−

=0

2

)/2()( π

Area under the standardized Gaussian

Page 3: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Error Function

Page 4: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Generalization to any confidence level

nherrorherrorzherror SS

NS))(1)(()( −

±

• Values of zN for 2-Sided N% Confidence IntervalsConfidence Level N%: 50% 68% 80% 90% 95% 98% 99%Constant zn: 0.67 1.00 1.28 1.64 1.96 2.33 2.58

Page 5: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Rule of thumb

• Binomial is approximated by Normal distribution as long as n >= 30 or when np(1-p) >= 5

• For smaller values of n it is wise to use a table giving exact values for the binomial distribution

Page 6: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Bivariate Normal Densities

Page 7: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when
Page 8: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

p(X1,X2) Is a hill-shaped surface

Page 9: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

LEVEL CURVES

• Slice the surface with horizontal planes which the locus of points with the quadratic form

Page 10: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when
Page 11: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when
Page 12: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when
Page 13: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when
Page 14: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when
Page 15: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

INFORMATION THEORY

Page 16: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Relative Entropy

Page 17: Gaussian Derivatives - cedar.buffalo.educedar.buffalo.edu/~srihari/CSE555/Normal2.pdf · Rule of thumb • Binomial is approximated by Normal distribution as long as n >= 30 or when

Mutual Information


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