dustinvtran
commented
8 years ago Good catch! Yes you're right, the prior is described incorrectly, with the most obvious reason being that there's a dimension mismatch in the equation.
If you have time to make edits, would greatly appreciate it and we can merge those changes into the website.
The description of GP classification here: http://edwardlib.org/tut_gp_classification seems to be incorrect. The description looks like Bayesian Logistic regression where the prior covariance matrix on the weights has been replaced with the Gram matrix of a GP covariance function. The dimensionality of z implied by p(z)=N(z;0,K) with K the Gram matrix is the number of data cases. x_n is stated to have dimension D. In that case, the inner product x_n'z in the inverse logit has a dimension mismatch. Compare to equation 3.10 in Rasmussen and Williams 2006 for their presentation of the posterior predictive distribution. In your notation, you probably want something like p(y_n|x_n,f)=Bernoulli(yn | logitinv(f(x_n))) with f the draw from GP, or p(y_n|x_n,z_n)=Bernoulli(yn | logitinv(z_n)) with z_n = f(x_n).