Cross-Validation--based Adaptive Sampling for Gaussian Process Models

In many real-world applications, we are interested in approximating black-box, costly functions as accurately possible with the smallest number of function evaluations. A complex computer code is an example such a function. this work, Gaussian process (GP) emulator used to approximate output code. We consider problem extending initial experiment (set model runs) sequentially improve emulator. sequential sampling approach based on leave-one-out (LOO) cross-validation proposed that can be easily extended batch mode. This desirable property since it saves user time when parallel computing available. After fitting GP training data points, expected squared LOO (ES-LOO) error calculated at each design point. ES-LOO measure identify important points. More precisely, quantity large point means quality prediction depends great deal and adding more samples nearby could accuracy GP. As result, reasonable select next sample where maximized. However, only known experimental needs estimated unobserved To do this, second fitted errors, maximum modified improvement (EI) criterion occurs chosen sample. EI popular acquisition Bayesian optimization trade off between local global search. has tendency towards exploitation, meaning its close (current) “best" avoid clustering, version EI, called pseudoexpected improvement, employed which explorative than yet allows us discover unexplored regions. Our results show method promising.