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

TL;DR

FunQuant is an R package designed to perform quantization efficiently in scenarios involving rare events and costly simulations, addressing the challenges of data approximation in such contexts.

Contribution

The paper introduces FunQuant, a novel R package that adapts quantization methods for rare event scenarios with expensive data evaluations.

Findings

Effective quantization of rare event data

Improved computational efficiency in costly simulations

Enhanced accuracy in probabilistic clustering

Abstract

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.