Efficient Estimation of the ANOVA Mean Dimension, with an Application to Neural Net Classification

DOI10.1137/20M1350236zbMath1464.62139arXiv2007.01281OpenAlexW3169055364MaRDI QIDQ4995121

Christopher R. Hoyt, Art B. Owen

Publication date: 23 June 2021

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.01281

zbMATH Keywords

global sensitivity analysischainingSobol' indicesexplainable AIpick-freezewinding stairs

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Nonparametric estimation (62G05) Artificial neural networks and deep learning (68T07) Monte Carlo methods (65C05) Analysis of variance and covariance (ANOVA) (62J10)

Related Items (2)

Global sensitivity analysis in epidemiological modeling ⋮ Screening: from tornado diagrams to effective dimensions

Uses Software

• TensorFlow
• Grad-CAM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sensitivity analysis: a review of recent advances
• Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index
• From screening to quantitative sensitivity analysis. A unified approach
• The jackknife estimate of variance
• The use of polynomial splines and their tensor products in multivariate function estimation. (With discussion)
• Making best use of model evaluations to compute sensitivity indices
• Analysis of variance designs for model output
• Sharp inequalities between skewness and kurtosis
• Estimation of global sensitivity indices for models with dependent variables
• Generalized Hoeffding-Sobol decomposition for dependent variables -- application to sensitivity analysis
• Shapley Effects for Global Sensitivity Analysis: Theory and Computation
• On Shapley Value for Measuring Importance of Dependent Inputs
• AN APPROXIMATION THEORETIC PERSPECTIVE OF SOBOL' INDICES WITH DEPENDENT VARIABLES
• Mean Dimension of Ridge Functions
• Asymptotic normality and efficiency of two Sobol index estimators
• Generalized Sobol sensitivity indices for dependent variables: numerical methods
• A quasi-Monte Carlo Metropolis algorithm
• Estimating Mean Dimensionality of Analysis of Variance Decompositions
• A Class of Statistics with Asymptotically Normal Distribution

This page was built for publication: Efficient Estimation of the ANOVA Mean Dimension, with an Application to Neural Net Classification