**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) $

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.

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.

Go up to basics of HMMs

Review of basic probability

“All models are wrong, but some are useful.” - George Box

- 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.

Review of Computing in Graphical Models: complexity analysis

Canceled for MLK Jr. Day

Computing in Graphical Models: binary tree model

Model Selection With Probabilistic Models

- See chapter on Model Comparison and Occam's Razor from David MacKay's book on

Information Theory and Inference, and video lecture of David lecturing on Bayesian inference.

Midterm Exam

Cancelled for President's Day holiday

continued Expectation Maximization:Singular Solutions

Hidden Markov Models* (See Murphy text chapter 17)

review of Hidden Markov Models* 10 minutes of Gibbs Sampling