Results 31 to 40 of about 21,675 (137)
Representing functional data in reproducing Kernel Hilbert Spaces with applications to clustering and classification [PDF]
Functional data are difficult to manage for many traditional statistical techniques given their very high (or intrinsically infinite) dimensionality. The reason is that functional data are essentially functions and most algorithms are designed to work ...
Alberto Muñoz, Javier González
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Scattering systems with several evolutions and formal reproducing kernel Hilbert spaces [PDF]
, 2013 A Schur-class function in $d$ variables is defined to be an analytic contractive-operator valued function on the unit polydisk. Such a function is said to be in the Schur--Agler class if it is contractive when evaluated on any commutative $d$-tuple of ...
Ball, Joseph A. +3 more
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Regularization in Reproducing Kernel Hilbert Spaces
, 2022 AbstractMethods for obtaining a functiongin a relationship$$y=g(x)$$y=g(x)from observed samples ofyandxare the building blocks for black-box estimation. The classical parametric approach discussed in the previous chapters uses a function model that depends on a finite-dimensional vector, like, e.g., a polynomial model.
Gianluigi Pillonetto +4 more
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Lepskii Principle in Supervised Learning
, 2019 In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the least-square ...
Blanchard, Gilles +2 more
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Learnability in Hilbert Spaces with Reproducing Kernels
Journal of Complexity, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Uniform Distribution, Discrepancy, and Reproducing Kernel Hilbert Spaces
Journal of Complexity, 2001 The results are related with numerical integration of functions in a reproducing kernel Hilbert space (RKHS). The authors define a notion of uniform distribution and discrepancy of sequences in an abstract set \(E\) in terms of a RKHS of functions on \(E\). In the case of the finite-dimensional unit cube the discrepancies introduced are closely related
Amstler, Clemens, Zinterhof, Peter
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Radial kernels and their reproducing kernel Hilbert spaces
Journal of Complexity, 2010 Let \(R\) be a continuous convex function on a Hilbert space \(H\). In learning theory, \[ A(\lambda):= \inf_{h\in H} \{\lambda\| h\|^2+ R(h)\}- \inf_{h\in H} R(h) \] is called an approximation error function. Here, \(H\) is a reproducing kernel Hilbert space (RKHS) of functions on \(\mathbb{R}^d\), i.e., such that the evaluations \(\delta_x: h\mapsto ...
Scovel, Clint +3 more
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A Characterization for reproducing kernel Hilbert spaces
Journal of Mathematical Analysis and Applications, 1974 AbstractLet G(t, s) be the Green's functions associated with N, a differential operator restricted to certain boundary conditions. Define (u, v)N = (Nu, v)L2. It is shown that the reproducing kernel Hilbert space generated by G is the same as the Hilbert-space completion with respect to ∥ · ∥N of the set of real valued functions which are in C2n and ...
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Flexible Expectile Regression in Reproducing Kernel Hilbert Spaces
Technometrics, 2017 Expectile, first introduced by Newey and Powell in 1987 in the econometrics literature, has recently become increasingly popular in risk management and capital allocation for financial institutions due to its desirable properties such as coherence and elicitability.
Yang, Yi, Zhang, Teng, Zou, Hui
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Nonparametric maximum likelihood estimation of probability densities by penalty function methods [PDF]
When it is known a priori exactly to which finite dimensional manifold the probability density function gives rise to a set of samples, the parametric maximum likelihood estimation procedure leads to poor estimates and is unstable; while the ...
Demontricher, G. F. +2 more
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