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A Generalized Representer Theorem for Hilbert Space - Valued Functions

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Criteria for the existence of a potential well

Charles Stuart

We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...

Pergamon-Elsevier Science Ltd2017

A generalized mountain-pass theorem: the existence of multiple critical points

Hans-Jörg Ruppen

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

Semi-supervised and unsupervised kernel-based novelty detection with application to remote sensing images

Frank Grégoire Jean de Morsier

The main challenge of new information technologies is to retrieve intelligible information from the large volume of digital data gathered every day. Among the variety of existing data sources, the satellites continuously observing the surface of the Earth ...

EPFL2014

Distributed machine learning in networks by consensus

Martin Hasler, Leonidas Georgopoulos

We propose an algorithm to learn from distributed data on a network of arbitrarily connected machines without exchange of the data-points. Parts of the dataset are processed locally at each machine, and then the consensus communication algorithm is employe ...

Elsevier2014

Explicit Recursive and Adaptive Filtering in Reproducing Kernel Hilbert Spaces

Devis Tuia

This brief presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces. Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define the model recursivity in the Hilbert spa ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Invariant manifolds with boundary for jump-diffusions

Damir Filipovic

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures. ...

Univ Washington, Dept Mathematics2014

On the eigenvalue decay of solutions to operator Lyapunov equations

Daniel Kressner

This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the kth (generalized) eigenvalue decays exponentially in root k, provided that the involved operator A gener ...

Elsevier Science Bv2014

Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting

Andreas Krause, Matthias Seeger

Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low norm in a reproducing ...

Institute of Electrical and Electronics Engineers2012

A Signal Processing Approach to Generalized 1-D Total Variation

Dimitri Nestor Alice Van De Ville, Fikret Isik Karahanoglu, Ilker Bayram

Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rat ...

Institute of Electrical and Electronics Engineers2011

Frame Domain Signal Processing: Framework and Applications

Martin Vetterli, Amina Chebira

Besides basis expansions, frames representations play a key role in signal processing. We thus consider the problem of frame domain signal processing, which is more complex and challenging than transform domain processing. Examples of such processing aboun ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010