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In this paper, we provide a precise characterization of generalizationproperties of high dimensional kernel ridge regression across the under- andover-parameterized regimes, depending on whether the number of training data nexceeds the feature dimension d. By establishing a bias-variance decompositionof the expected excess risk, we show that, while the bias is (almost)independent of d and monotonically decreases with n, the variance depends on n,d and can be unimodal or monotonically decreasing under differentregularization schemes. Our refined analysis goes beyond the double descenttheory by showing that, depending on the data eigen-profile and the level ofregularization, the kernel regression risk curve can be a double-descent-like,bell-shaped, or monotonic function of n. Experiments on synthetic and real dataare conducted to support our theoretical findings.

Kernel regression in high dimensions: Refined analysis beyond double descent