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Charlie SIRE committed Jul 12, 2023
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Expand Up @@ -50,9 +50,9 @@ $$\frac{\frac{1}{n} \sum^{n}_{k=1} Y(\tilde{X}_{k})\mathbb{1}_{Y(\tilde{X}_{k})\
where $f_{X}$ is the known density function of the inputs $X$, and $(\tilde{X}_k)^{n}_{k=1}$ i.i.d. random variables of density function $g$.
Importance Sampling is employed with the aim of reducing the variance of the estimators of the centroids when compared to classical Monte Carlo methods. FunQuant provides various approaches for implementing these estimators, depending on the sampling density denoted as $g$. The simplest method involves using the same function $g$ for each iteration and every cluster, which is straightforward to work with and still yields significant variance reduction. More advanced implementations enable the adaptation of the sampling density for each cluster at every iteration.

In addition, FunQuant is designed to mitigate the computational burden associated with the evaluation of costly data. While users have the flexibility to utilize their own metamodels to generate additional data, FunQuant offers several functions tailored specifically for a metamodel dedicated to spatial outputs such as maps. This metamodel relies on Functional Principal Component Analysis and Gaussian Processes, based on the work of [@Perrin], adapted with the rlibkriging R package [@rlib]. FunQuant assists in the fine-tuning of its hyperparameters for a quantization task, with different performance metrics involved.
In addition, FunQuant is designed to mitigate the computational burden associated with the evaluation of costly data. While users have the flexibility to utilize their own metamodels to generate additional data, FunQuant offers several functions tailored specifically for a metamodel dedicated to spatial outputs such as maps. This metamodel relies on Functional Principal Component Analysis and Gaussian Processes, based on the work of @Perrin, adapted with the rlibkriging R package [@rlib]. FunQuant assists in the fine-tuning of its hyperparameters for a quantization task, with different performance metrics involved.

Additional theoretical information can be found in [@sire]. The paper provides a comprehensive exploration of the application of FunQuant to the quantization of flooding maps.
Additional theoretical information can be found in @sire. The paper provides a comprehensive exploration of the application of FunQuant to the quantization of flooding maps.



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