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A Martingale Kernel Independence Test

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arXiv:2605. 22549v1 Announce Type: new Abstract: The Hilbert-Schmidt Independence Criterion (HSIC) and its joint-independence extension $d\mathrm{HSIC}$ are degenerate $V$-statistics whose data-dependent weighted-$\chi^2$ null limits force a permutation calibration that multiplies the per-test cost by the number of permutations, in practice two orders of magnitude.