Interpolation and Learning with Scale Dependent Kernels

Understand

We study the learning properties of nonparametric ridge-less least squares.

• In particular, we consider the common case of estimators defined by scale dependent kernels, and focus on the role of the scale.
• These estimators interpolate the data and the scale can be shown to control their stability through the condition number.
• Our analysis shows that are different regimes depending on the interplay between the sample size, its dimensions, and the smoothness of the problem.