FunQuant: A R package to perform quantization in the context of rare events and time-consuming simulations

Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be seen as clusters, and constructs a discrete distribution based on their centroids and probabilistic masses. Lloyd's algorithm estimates the optimal centroids in a minimal expected distance sense, but this approach poses significant challenges in scenarios where data evaluation is costly, and relates to rare events. Then, the single cluster associated to no event takes the majority of the probability mass. In this context, a metamodel is required and adapted sampling methods are necessary to increase the precision of the computations on the rare clusters.

Adaptive Design of Experiments for Conservative Estimation of Excursion Sets

We consider a Gaussian process model trained on few evaluations of an expensive-to-evaluate deterministic function and we study the problem of estimating a fixed excursion set of this function. We focus on conservative estimates as they allow control on false positives while minimizing false negatives. We introduce adaptive strategies that sequentially selects new evaluations of the function by reducing the uncertainty on conservative estimates. Following the Stepwise Uncertainty Reduction approach we obtain new evaluations by minimizing adapted criteria. We provide tractable formulae for the conservative criteria and we benchmark the method on random functions generated under the model assumptions in two and five dimensions. Finally the method is applied to a reliability engineering test case. Overall, the proposed strategy of minimizing false negatives in conservative estimation achieves competitive performance both in terms of model based and a-posteriori indicators.