Leveraging replication in active learning

Abstract

Many time-consuming simulators exhibit a complex noise structure that depends on the inputs. Advances in Gaussian process modeling with input-dependent noise, especially via replication (iid repetitions of the same experiment), allow efficient modeling with better uncertainty quantification on the predictions. We focus here on strategies for balancing replication, exploitation and exploration for various sequential design goals, possibly in parallel batches. These goals include global model accuracy, optimization, contour finding, and dimension reduction. Illustration on synthetic examples are provided as well as a large scale massively parallel real world epidemiology problem.

References:

• Ozik, Jonathan, et al. "A population data-driven workflow for COVID-19 modeling and learning." The International Journal of High Performance Computing Applications 35.5 (2021): 483-499.

• Binois, Mickael, Robert B. Gramacy, and Mike Ludkovski. "Practical heteroscedastic Gaussian process modeling for large simulation experiments." Journal of Computational and Graphical Statistics 27.4 (2018): 808-821.

• Binois, Mickaël, et al. "Replication or exploration? Sequential design for stochastic simulation experiments." Technometrics 61.1 (2019): 7-23.

• Binois, Mickael, Nicholson Collier, and Jonathan Ozik. "A portfolio approach to massively parallel Bayesian optimization." arXiv preprint arXiv:2110.09334 (2021).

Notes

• Personal website can be found here.