Gaussian process regression

[avehtari]

@linas

The original problem was to find important variables. My intention was to use ARD for this.

ARD is also a bad measure for relevance as it measures mostly non-linearity [1510.04813] Projection predictive model selection for Gaussian processes (published in Projection predictive model selection for Gaussian processes | IEEE Conference Publication | IEEE Xplore)

@linas

However for 5000 observations and 14 variables with a binomial likelihood

With that ratio, no need for MCMC. Use something like GPy, GPflow or in R CRAN - Package gplite

@linas

My understanding is that the algorithms in both articles require to estimate PPD. In case I have a squared exponential kernel with different length scales I gain nothing with respect to computational time. Perhaps if I use radial basis function kernel instead to estimate PPD for training points with Stan I could reduce computational burden. Then I could apply ideas from the older paper. Right?

Sorry, I don’t understand what you are saying.

If you want to model all interactions, have binomial observation model, 5000 observations and 14 variables, use something else than Stan.

If you are happy with an additive model, have binomial observation model, 5000 observations and 14 variables, you can try the basis function approximated GP also in Stan (probably good to use glm compound functions for speedup).