Abstract:  We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent (Matern) kernels, and focus on the role scale and smoothness. These estimators interpolate the data and the scale can be shown to control their stability to noise and sampling.  Larger scales, corresponding to smoother functions, improve stability with respect to sampling. However, smaller scales, corresponding to more complex functions, improve stability to noise. We will discuss to which extent these results can explain the learning curves observed for large overparameterized models.  Our analysis combines, probabilistic results with analytic techniques from interpolation theory.
 

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