Michael Data

Official Class Website

Program Description

Last year's class notes

Professor's Background Notes

Tricks

Trace Trick

The trace is the sum of the diagonals of a matrix. $tr(A) = \sum_i A_{i,i}$

The trace operator has the cyclic permutation property: $tr(x^T A x) = tr(A x^T x) = tr(x^T x A)$

See Kevin Murphy text page 99.

Dealing with http://en.wikipedia.org/wiki/Mahalanobis_distance Mahalanobis terms

Expand out $(x-\mu)^T\Sigma^{-1}(x-\mu)$ into $(x^T\Sigma^{-1}x) - (x^T\Sigma^{-1}\mu) - (\mu^T\Sigma^{-1}x) + (\mu^T\Sigma^{-1}\mu) $

Midterm

Only need to bring writing instruments.

Test is through Lecture 10, Model Selection With Probabilistic Models

In principle, can only study homeworks and class notes. Additional reading should help.

Notes on review of my midterm

A d-by-d covariance matrix can be stored using $\frac{d^2}{2}$ parameters due to symmetry.

For $K$ models in problem 3.2, Bayesian Model Averaging.

Final

Go up to basics of HMMs

Lecture 1

Review of basic probability

Lecture 2
Lecture 3

Multivariate Gaussian Model

  • See Murphy text p97-98, Barber p169

The key to learning is writing down a likelihood. Then the full Bayesian model is just icing afterword.

Learning from Data

Lecture 4
Lecture 5

Canceled for MLK Jr. Day

Lecture 6
Lecture 7
Lecture 8
Lecture 9
Lecture 10
Lecture 11

Midterm Exam

Lecture 12
Lecture 13

Cancelled for President's Day holiday

Lecture 14
Lecture 15
Lecture 16
Lecture 17
Lecture 18
Lecture 19
Lecture 20

review of Hidden Markov Models*
10 minutes of Gibbs Sampling