FunQuant: A R package to perform quantization in the context of rare events and time-consuming simulations
This work addresses a specific problem in statistical computing for researchers dealing with rare events and expensive simulations, representing an incremental improvement by adapting existing quantization techniques.
The paper tackles the challenge of performing quantization when data evaluation is costly and involves rare events, where traditional methods like Lloyd's algorithm struggle due to imbalanced probability masses. It introduces FunQuant, an R package that uses metamodels and adapted sampling methods to improve precision in such scenarios.
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 Voronoï 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.