Reproducing kernel Hilbert spaces

By Ronald Christensen. 2019

185 citations recorded by the source corpus.

This chapter introduces an elegant mathematical theory that has been developed for nonparametric regression with penalized estimation.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical Learning Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Francis R. Bach
2. Dag Tjøstheim
3. Jing Lei

In Computational Theory and Mathematics

1. Francis R. Bach
2. Ravi Ramamoorthi
3. Jonathan T. Barron
4. Peter Richtárik
5. Martin Jaggi
6. Nicolas Loizou
7. Simon Lacoste-Julien
8. Zeyuan Allen-Zhu

In Statistical Learning Theory

1. Francis R. Bach
2. Dag Tjøstheim
3. Haakon Otneim
4. Baard Stove
5. Kenji Fukumizu
6. Arthur Gretton
7. Bharath K. Sriperumbudur
8. Bernhard Schölkopf

Citations in the corpus

• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains (2020, background): “Kernel regression is a classic nonlinear regression algorithm [40].”
• On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, background): “This RKHS has two important characteristic properties (see, e.g., Berlinet and Thomas-Agnan, 2004): (a) Membership of kernel evaluations : for any x ∈ X , the function k ( , x ) : y 7→ k ( y, x ) is an element of F .”
• Statistical Dependence: Beyond Pearson’s ρ (2018, background): “A general reference to applications in statistics is Berlinet and Thomas-Agnan (2004).”