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What is Learnable in Valiant's Theory of the Learnable? 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Kernel-based method for joint independence of functional variables
Terence Kevin Manfoumbi Djonguet, Guy Martial Nkiet · 2022-08-15 · via math.ST updates on arXiv.org

This work investigates the problem of testing whether $d$ functional random variables are jointly independent using a modified estimator of the $d$-variable Hilbert Schmidt Indepedence Criterion ($d$HSIC) which generalizes HSIC for the case where $d \geq 2$. We then get asymptotic normality of this estimator both under joint independence hypothesis and under the alternative hypothesis. A simulation study shows good performance of the proposed test on finite sample.

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