# Michael's Wiki

##### 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

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

##### Lecture 3
• 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.

##### Lecture 4

Review of Computing in Graphical Models: complexity analysis

##### Lecture 5

Canceled for MLK Jr. Day

##### Lecture 10

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

Midterm Exam

##### Lecture 13

Cancelled for President's Day holiday

##### Lecture 15
• See Murphy text chapter 8
##### Lecture 19

Hidden Markov Models* (See Murphy text chapter 17)

##### Lecture 20

review of Hidden Markov Models* 10 minutes of Gibbs Sampling 