Taming Nonconvexity in Kernel Feature Selection -- Favorable Properties of the Laplace Kernel. (arXiv:2106.09387v3 [math.ST] UPDATED)

Kernel-based feature selection is an important tool in nonparametric
statistics. Despite many practical applications of kernel-based feature
selection, there is little statistical theory available to support the method.
A core challenge is the objective function of the optimization problems used to
define kernel-based feature selection are nonconvex. The literature has only
studied the statistical properties of the \emph{global optima}, which is a
mismatch, given that the gradient-based algorithms available for nonconvex
optimization are only able to guarantee convergence to local …

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