Laplace approximation for logistic Gaussian process density estimation and regression

Bayesian Modeling with Gaussian Processes using the GPstuff Toolbox

“…However, the implementation in GPstuff is unique and contains several practical solutions for computational problems that are not published elsewhere. Our own contribu-tion on GP theory that is included in GPstuff is described mainly in (Vehtari, 2001;Vehtari and Lampinen, 2002;Vanhatalo and Vehtari, 2007, 2008Vanhatalo et al, 2009Jylänki et al, 2011;Riihimäki and Vehtari, 2012;Joensuu et al, 2012;Joensuu et al, 2014;Riihimäki and Vehtari, 2014) Our intention has been to create a toolbox with which useful, interpretable results can be produced in a sensible time. GPstuff provides approximations with varying level of accuracy.…”

“…Logistic Gaussian process can be used for flexible density estimation and density regression. GPstuff includes implementation based on Laplace (and MCMC) approximation as described in (Riihimäki and Vehtari, 2012).…”

“…We use finite-dimensional approximation and evaluate the integral and the Gaussian process in a grid. We approximate inference for logistic Gaussian process density estimation in a grid using Laplace's method or MCMC to integrate over the non-Gaussian posterior distribution of latent values (see details in Riihimäki and Vehtari, 2012).…”