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 However, I was informed that the URL was no longer valid.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.
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