Approximating high-dimensional infinite-order U-statistics: statistical and computational guarantees
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We study the problem of distributional approximations to high-dimensional non-degenerate U-statistics with random kernels of diverging orders. Infinite-order U-statistics (IOUS) is a useful tool for constructing simultaneous prediction intervals that quantify the uncertainty of ensemble methods such as subbagging and random forests. A major obstacle in using the IOUS is their computational intractability when the sample size, dimensionality, and order, are all large. In this article, we derive non-asymptotic Gaussian approximation error bounds for an incomplete version of the IOUS with a random kernel. We also study data-driven inferential methods for the incomplete IOUS via bootstraps with statistical and computational guarantees.
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