For interpolating kernel machines, the minimum norm ERM solution is the most stable
Name
CBMM_Memo_108.pdf
Size
1015.14 KB
Format
Adobe PDF
Checksum (MD5)
3223c4e6a61f5f6002aa477e149e6efe
Author(s)
Rangamani, Akshay
Rosasco, Lorenzo
Poggio, Tomaso
Date Issued
June 22, 2020
Publisher
Center for Brains, Minds and Machines (CBMM)
Series/Report no.
CBMM Memo;108
Abstract
We study the average CVloo stability of kernel ridge-less regression and derive corresponding risk bounds. We show that the interpolating solution with minimum norm has the best CVloo stability, which in turn is controlled by the condition number of the empirical kernel matrix. The latter can be characterized in the asymptotic regime where both the dimension and cardinality of the data go to infinity. Under the assumption of random kernel matrices, the corresponding test error follows a double descent curve.
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