Someone asked me "why did you say in the Gaussian processes tutorial that Gaussian processes are ill-conditioned?" Here is an answer in the form of a tiny exercise.

Take the simplest case where the function is just a constant.

y(x) = Y for all x. (Y is Gaussian distributed and not known a priori)

Make a GP with the appropriate covariance function.

Now

(1) think about the inference of the GP given data {x,t}. (Not very difficult is it?)

(2) see what happens when you use the standard GP matrix inversion formalism to solve the problem. What is the well-conditioned-ness of the matrix you must invert?

## 2 comments:

Dear Mr. McKay,

I really enjoyed the SEWTHA book (about half done now) and was going to get "the other book". However, I was informed that the URL was no longer valid.

Jim Riddell

Very Nice And Interesting Post, thank you for sharing.

Short Inspirational Quotes - Gym Quotes

Best Quotes - Future Quotes - xyore

Image Bank - Positive Life Quotes

Success Quotes - حكمة اليوم

كلام جميل - حكم عن الحياة

Post a Comment