# Efficient estimation of the ANOVA mean dimension, with an application to neural net classification

@article{Hoyt2021EfficientEO, title={Efficient estimation of the ANOVA mean dimension, with an application to neural net classification}, author={Christopher R. Hoyt and Art B. Owen}, journal={SIAM/ASA J. Uncertain. Quantification}, year={2021}, volume={9}, pages={708-730} }

The mean dimension of a black box function of $d$ variables is a convenient way to summarize the extent to which it is dominated by high or low order interactions. It is expressed in terms of $2^d-1$ variance components but it can be written as the sum of $d$ Sobol' indices that can be estimated by leave one out methods. We compare the variance of these leave one out methods: a Gibbs sampler called winding stairs, a radial sampler that changes each variable one at a time from a baseline, and a…

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