Happy THOR DAY!!

Ok, Mom, here is your post ;)

So this past week has been spent on two things:

Machine Learning Homework - I don't know what is going on in this class. It is like being told: "if you move your hands, water moves" and then getting thrown in to a pool... of d dimentional space. It stinks.

Computational Photography Project - I know a little more about this. We are implementing Poisson Blending to insert an image over another. It is a really cool effect, but really math intensive. Also lots of number crunching. I filled up all of the 4 GB of system memory on my computer crunching the outcome of 70,000 equations with 30,000 unknowns before I knew about "sparse" matricies. However as of last night I hit a little brick wall. Fear not, this morning walking to the bus, I had a "moment of clarity" and I think I know how to solve the issue I am having.

Other than that I been doing these things:
Sleeping (unfortunately not very much)
Eating (not very well, and at odd hours... good thing there are no grape nuts around)
Showering (don't worry, I will always be clean)
Getting very apprciated pick-me-ups from Brian, Grandma and Gramps, Chelsea, Jamie, James, and my apparent life guard Kirsten.
And blowing my nose (either a cold or allergies have infested my nose with mucus)


So... now back to work...

3.2 Multivariate Gaussian Distribution
The density function of a p-dimensional Gaussian distribution is as follows:
N(x|mu,A^-1) := 1/((2pi)^(p/2) * (|A^-1|)^(1/2)) * e ^ (-1/2 * (x-mu)^T A (x-mu))
where A is the inverse of the covariance matrix, or the so-called precision matrix. Let {x1,x2,...xn} be i.i.d sample from a p-dimensional Gaussian distribution.
1) Suppose that n >> p. Derive the MLE estimates for mu and A.


... don't know what the means? Yeah, neither do I.