Empirical two-sample error for powered even-order Gromov-Wasserstein functionals is bounded by n^{-2/max{min(d_x,d_y),4}} up to logs when min dimension equals 4.
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At the symmetrization interface in VC learning, the ghost-gap bad event is analytic (hence null-measurable w.r.t. finite Borel measures) for Borel-parameterized classes on Polish spaces, with a strict separation from Borel and closure under natural constructors.
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Empirical Convergence of Even-Order Gromov-Wasserstein Functionals
Empirical two-sample error for powered even-order Gromov-Wasserstein functionals is bounded by n^{-2/max{min(d_x,d_y),4}} up to logs when min dimension equals 4.
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Null Measurability at the Symmetrization Interface in VC Learning
At the symmetrization interface in VC learning, the ghost-gap bad event is analytic (hence null-measurable w.r.t. finite Borel measures) for Borel-parameterized classes on Polish spaces, with a strict separation from Borel and closure under natural constructors.