Gaussian Processes

Gaussian Process based Kriging Believer achieved performance statistically indistinguishable from joint q-EI on Hartmann-6D. Variance reduction in the Gaussian Process posterior is identified as the main driver of batch diversity. A pseudo-observation reduces posterior variance at the selected point and around it through posterior covariance. Gaussian Process posterior conditioning identities provide the canonical implementation of efficient conditioning. Acquisition functions such as EI, UCB, and PI are depressed near the selected pseudo-observation because they are monotone in uncertainty for fixed mean.