- Tytuł:
- Decomposition of Gaussian processes, and factorization of positive definite kernels
- Autorzy:
-
Jorgensen, Palie E. T.
Tian, Feng - Powiązania:
- https://bibliotekanauki.pl/articles/255819.pdf
- Data publikacji:
- 2019
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
reproducing kernel Hilbert space frames
generalized Ito-integration
the measurable category analysis/synthesis
interpolation
Gaussian free fields
non-uniform sampling
optimization
transform
covariance
feature space - Opis:
- 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.
- Źródło:
-
Opuscula Mathematica; 2019, 39, 4; 497-541
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł