For interpolating kernel machines, minimizing the norm of the ERM solution minimizes stability

• URL: http://arxiv.org/abs/2006.15522v2
• Date: Sun, 11 Oct 2020 22:58:31 GMT
• Title: For interpolating kernel machines, minimizing the norm of the ERM solution minimizes stability
• Authors: Akshay Rangamani, Lorenzo Rosasco, Tomaso Poggio
• Abstract summary: We show that the interpolating solution with minimum norm minimizes a bound on $mboxCV_loo$ stability. Under the assumption of random kernel, the corresponding test error should be expected to follow a double descent curve.
• Score: 20.775719987269003
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the average $\mbox{CV}_{loo}$ stability of kernel ridge-less regression and derive corresponding risk bounds. We show that the interpolating solution with minimum norm minimizes a bound on $\mbox{CV}_{loo}$ 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 should be expected to follow a double descent curve.

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