<ul><li>Kernel ridge regression (KRR) is a fundamental method for learning functions from finite samples.</li><li>A comprehensive study of KRR in the noiseless regime reveals optimal convergence rates determined by eigenvalue decay and target function's smoothness.</li><li>KRR exhibits extra-smoothness compared to typical functions in the native reproducing kernel Hilbert space (RKHS).</li><li>A novel error bound for noisy KRR achieves minimax optimality in both noiseless and noisy regimes.</li></ul>

Optimal Rates and Saturation for Noiseless Kernel Ridge Regression

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