Where can I find details of the algorithm used in the algebra solver? I found the new section in the stan-reference, but it doesn’t mention anything about the algorithm (I added a issue comment about this). Quick look at the github didn’t help either. I’m asking if it would be good for solving
0 = f - K ∇ log p(y | f)
where f is a vector of n latent values, K is a n x n covariance matrix, ∇ log p(y | f) is a vector of first derivatives of the likelihood wrt f, and usually n>1000. Usually this is solved with Newton’s method, but I’m guessing that the algorithm in algebra_solver probably would not be as good for this specific problem?
And for those who don’t know yet, solving the above equation finds the posterior mode for the latent values in Gaussian latent variable model with a non-Gaussian likelihood, which could be used as part of the Laplace approximation for GMRF’s and GP’s with non-Gaussian likelihoods. Extra cool would be possibility to give the log likelihood as an argument and let the autodiff compute the first derivative ∇ log p(y | f).