  Gaussian process (GP) surrogate modeling for large computer experiments is
limited by cubic runtimes, especially with data from stochastic simulations
with input-dependent noise. A popular workaround to reduce computational
complexity involves local approximation (e.g., LAGP). However, LAGP has only
been vetted in deterministic settings. A recent variation utilizing inducing
points (LIGP) for additional sparsity improves upon LAGP on the
speed-vs-accuracy frontier. The authors show that another benefit of LIGP over
LAGP is that (local) nugget estimation for stochastic responses is more
natural, especially when designs contain substantial replication as is common
when attempting to separate signal from noise. Woodbury identities, extended in
LIGP from inducing points to replicates, afford efficient computation in terms
of unique design locations only. This increases the amount of local data (i.e.,
the neighborhood size) that may be incorporated without additional flops,
thereby enhancing statistical efficiency. Performance of the authors' LIGP
upgrades is illustrated on benchmark data and real-world stochastic simulation
experiments, including an options pricing control framework. Results
indicatethat LIGP provides more accurate prediction and uncertainty
quantification for varying data dimension and replication strategies versus
modern alternatives.
