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What is Learnable in Valiant's Theory of the Learnable? 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Decoupling and randomization for double-indexed permutation statistics
Mingxuan Zou, Jingfan Xu, Peng Ding, Fang Han · 2026-01-28 · via math.ST updates on arXiv.org

This paper introduces a version of decoupling and randomization to establish concentration inequalities for double-indexed permutation statistics. The results yield, among other applications, a new combinatorial Hanson-Wright inequality and a new combinatorial Bennett inequality. Several illustrative examples from rank-based statistics, graph-based statistics, and causal inference are also provided.

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