4. Gaussian models

Question 1

<b>Introduction</b>
Basics
- MVN def
- Mahalanobis distance in the MVN
- eigendecomposition of covariance matrix
- How eigenvectors, eigenvalues, and mu affect the countours of equal probability density of a Gaussian

Answer 1

p. 99

Question 2

<b>Introduction</b>

MLE for an MVN

Answer 2

p. 101

Question 3

<b>Gaussian discriminant analysis</b>

• class conditional density in the GDA
• when GDA is equivalent do naive Bayes?
• why GDA can be thought of as a nearest centroids classifier?
• the formula to classify a new test vector in GDA assuming a uniform prior.

Answer 3

p. 103

Question 4

<b>Gaussian discriminant analysis</b>
Quadratic discriminant analysis (QDA)
- posterior over class labels in QDA

Answer 4

p. 104

Question 5

<b>Gaussian discriminant analysis</b>
Linar discriminant analysis (LDA)
- LDA as a special case of QDA
- LDA and softmax function
- Softmax and Boltzmann distribution

Answer 5

p. 105

Question 6

<b>Gaussian discriminant analysis</b>
Two-class LDA

Answer 6

p. 106

Question 7

<b>Gaussian discriminant analysis</b>

MLE for discriminant analysis

Answer 7

p. 108

Question 8

<b>Gaussian discriminant analysis</b>

Strategies for preventing overfitting

Answer 8

p. 108

Question 9

<b>Gaussian discriminant analysis</b>

Regularized LDA

Answer 9

p. 109

Question 10

<b>Gaussian discriminant analysis</b>

Diagonal LDA

Answer 10

p. 110

Question 11

<b>Inference in jointly Gaussian distributions</b>

Answer 11

p. 112