Reformulation variational lower bound in gpLogLikelihood.m

[SimonEbner]

Dear all,

first of all, thank you very much for providing your code as open source. It's very impressive and educational. I have a quick question concerning the calculation of the first part of the variational lower bound in gpLogLikelihood.m:54:

  ll =  -0.5*(model.d*(-(model.N-model.k)*log(model.beta) ...
                       - model.logDetK_uu +model.logdetA) ...
              - (sum(sum(model.Ainv.*EET)) ...
                 -sum(sum(model.m.*model.m)))*model.beta)   ;

As far as I understand it, this is a reformulation of

 F = log[ N( y| 0, sigma^2 * I + Q_nn )] with Q_nn = K_nm / K_mm K_mn

Do you happen to have a article / paper for me which helps me understanding the mathmatical reformulation that are going on here?

Thank you very much in advance.
Best,
Simon

[adamian]

Hi Simon,

Check these two papers:
Titsias 09 - Variational Learning of Inducing Variables in Sparse Gaussian
Processes
Lawrence 07 - Learning for Larger Datasets with the Gaussian Process Latent Variable Model

Hope this helps!
Andreas

[SimonEbner]

Hi Andreas,

thank you very much, I hadn't looked at the second paper. It made things clear now.

Best, Simon