Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
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PAIR-CI restores calibration to conditional independence testing under missing data by using paired permutations that force imputation error to cancel in the loss difference, together with a consistent variance estimator that unifies cross-validation and imputation uncertainty.
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Large Dimensional Kernel Ridge Regression: Extending to Product Kernels
Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
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PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Data
PAIR-CI restores calibration to conditional independence testing under missing data by using paired permutations that force imputation error to cancel in the loss difference, together with a consistent variance estimator that unifies cross-validation and imputation uncertainty.