Decomposition of Gaussian processes, and factorization of positive definite kernels

• Autorzy: Jorgensen Palie E. T. , Tian Feng

Identyfikatory

DOI

10.7494/OpMath.2019.39.4.497

• Języki publikacji: EN

Abstrakty

EN

We establish a duality for two lactorization questions, one for general positive definite (p.d.) kernels K, and the other for Gaussian processes, say V. The latter notion, for Gaussian processes is stated via Ito-integration. Our approach to factorization for p.d. kernels is intuitively motivated by matrix factorizations, but in infinite dimensions, subtle measure theoretic issues must be addressed. Consider a given p.d. kernel K, presented as a covariance kernel for a Gaussian process V. We then give an explicit duality for these two seemingly different notions of factorization, for p.d. kernel K, vs for Gaussian process V. Our result is in the form of an explicit correspondence. It states that the analytic data which determine the variety of factorizations for K is the exact same as that which yield factorizations for V. Examples and applications are included: point-processes, sampling schemes, constructive discretization, graph-Laplacians, and boundary-value problems.

Słowa kluczowe

EN

reproducing kernel Hilbert space frames; generalized Ito-integration; measurable category analysis/synthesis; interpolation; Gaussian free fields; non-uniform sampling; optimization; transform; covariance; feature space

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 4
• Strony: 497--–541
• Opis fizyczny: Bibliogr, 76 poz.

Twórcy

autor

Jorgensen Palie E. T.

• The University ol Iowa Department ol Mathematics Iowa City, IA 52242-1419, USA

autor

Tian Feng

• Hampton University Department of Mathematics Hampton, VA 23668, USA

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