Learning Sets with Separating Kernels
By Ernesto De Vito, Lorenzo Rosasco, Alessandro Toigo. 2012
57 citations recorded by the source corpus.
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of reproducing kernel, that we call separating kernel, plays a crucial role in our study and is analyzed in detail. We prove a new analytic characterization of the support of a distribution, that naturally leads to a family of provably consistent regularized learning algorithms and we discuss the stability of these methods with respect to random sampling. Numerical experiments show that the approach is competitive, and often better, than other state of the art techniques.
Subfields: Artificial Intelligence, Computational Mechanics, Statistics and Probability
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Citations in the corpus
- Separability of reproducing kernel spaces (2015, background): “For example, Steinwart and Christmann’s [33, Thm. 7.22] oracle inequality for SVMs, Christmann and Steinwart [8, Thms. 7 & 12], [7], [6], Steinwart and Christmann [34], [35], De Vito, Rosasco and Toigo [9], Hable and Christmann [18, Thm. 3.2], Lukić and Beder [25], Steinwart [32] and Vovk [38, Thm.”
- Exponential convergence of testing error for stochastic gradient methods (2017, unknown): “Finally note that the results of this section can be easily generalized from X = R d to any Polish space, by using a separating kernel (De Vito et al., 2014; Rudi et al., 2014) instead of (A6) .”