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.

So you are alive!!! I think the only help I can give you on the equation is that 1/2 = .5 last time I looked. Sorry. But at least I thought to wish you Happy Thor Day!!!! XOXOX Mom

ReplyDeleteTo obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. So there!!!!!

ReplyDeleteYeah but, .5 also equals50% too! So that kind of math writing is actually real?

ReplyDeleteLooks interesting, remember that you'll soon have all that new math learned. Right???

TheforK

There you go ... hurting my brain again!!!

ReplyDeleteAuntie Donna, he is hurting my brain also, except that he is asking me for help!!! Scottie, do you remember it has been 8 years since I took linear algebra? But this is fun, I'm glad you asked me.

ReplyDeleteBest quote of my helping Scott over Skype:

ReplyDelete[9:33:34 AM] Chelsea: Yes, I think you should have "all of the bs in the same form..." (quoted from Scott)