Predicting kernel spectra powerlaw exponents from raw data statistics

This is a technical note on kernel theory. Venture in at your own risk! My collaborators and I recently put out a paper called Predicting kernel regression learning curves from raw data statistics in which, among other things, we show how to map from the data PCA stats to the eigenfunctions and eigenvalues of a broad swath of rotation-invariant kernels. It’s a surprising result, both…