Effect of Data Dependence on KRR Generalization

Determine whether statistical dependencies among training samples arising when each independently sampled signal is paired with k independently sampled noise realizations to produce observations g(x,u) benefit or hinder the generalization performance of kernel ridge regression.

Background

The paper highlights that most existing generalization theory for kernel ridge regression (KRR) assumes independently and identically distributed data, whereas many real-world applications—such as denoising score learning—produce multiple noisy observations from the same underlying signal, leading to dependent training samples.

Within this structured non‑i.i.d. setting (each signal x is paired with k i.i.d. noises u to form observations g(x,u)), the authors note that it had not been systematically studied whether such dependencies help or harm KRR generalization, motivating their analysis and results.