2024/07/05 by Lamboni, Matieyendou
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Optimization and Control (math.OC) #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2407.11035
Computing cross-partial derivatives using fewer model runs is relevant in modeling, such as stochastic approximation, derivative-based ANOVA, exploring complex models, and active subspaces. This paper introduces surrogates of all the cross-partial derivatives of functions by evaluating such functions at N randomized points and using a set of L constraints. Randomized points rely on independent, central, and symmetric variables. The associated estimators, based on NL model runs, reach the optimal rates of convergence (i.e., O(N-1)), and the biases of our approximations do not suffer from the curse of dimensionality for a wide class of functions. Such results are used for i) computing the main and upper-bounds of sensitivity indices, and ii) deriving emulators of simulators or surrogates of functions thanks to the derivative-based ANOVA. Simulations are presented to show the accuracy of our emulators and estimators of sensitivity indices. The plug-in estimates of indices using the U-statistics of one sample are numerically much stable.