# Kernel-based measures of association between inputs and outputs based on ANOVA

arXiv: https://arxiv.org/abs/2311.14894 · HTML: https://mlsanity.com/paper/2311.14894/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2023.

## Built on by (most cited first, 3 of 3)

- [Optimal estimators of cross-partial derivatives and surrogates of functions](https://mlsanity.com/paper/2407.11035/) (2024)
- [Hybrid Uncertainty Sensitivity Analysis Based on the HSIC for High-Dimensional Responses with Aleatory--Epistemic Separation](https://mlsanity.com/paper/2606.14053/) (2026)
- [A Weighted Kernel Method for Approximation that Adapts to Learned Multivariable Structure](https://mlsanity.com/paper/2609.16606/) (2026)

## Abstract (arXiv)

ANOVA decomposition of function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate reproducing kernel Hilbert space regarding their distributions, we propose an efficient statistical test of independence between the input variables and output variable(s). The resulting test statistic leads to new dependent measures of association between inputs and outputs that allow for i) dealing with any distribution of AFs, including the Cauchy distribution, ii) accounting for the necessary or desirable moments of AFs and the interactions among the input variables. In uncertainty quantification for mathematical models, a number of existing measures are special cases of this framework. We then provide unified and general global sensitivity indices and their consistent estimators, including asymptotic distributions. For Gaussian-distributed AFs, we obtain Sobol' indices and dependent generalized sensitivity indices using quadratic kernels.