Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Toni Karvonen"'
Publikováno v:
Mathematics of Computation. 90:2209-2233
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an algorithm fo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6bb5c5b9d37b1f7e7370dabe4eaaeea
https://doi.org/10.1090/mcom/3659
https://doi.org/10.1090/mcom/3659
Publikováno v:
Numerical Algorithms. 87:445-468
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel interpola
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::02514bca553c66f533daa248cad1f65b
https://doi.org/10.1007/s11075-020-00973-y
https://doi.org/10.1007/s11075-020-00973-y
Publikováno v:
MLSP
Markov chain Monte Carlo (MCMC) methods are a cornerstone of Bayesian inference and stochastic simulation. The Metropolis-adjusted Langevin algorithm (MALA) is an MCMC method that relies on the simulation of a stochastic differential equation (SDE) w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::af31fb21a0deef8b2fbf1468d68cd1b5
https://doi.org/10.1109/mlsp52302.2021.9596301
https://doi.org/10.1109/mlsp52302.2021.9596301
This article is concerned with Gaussian filtering in nonlinear continuous-discrete state-space models. We propose a novel Taylor moment expansion (TME) Gaussian filter, which approximates the moments of the stochastic differential equation with a tem
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a23c0b7ba2a18fc92bf55b3b28b3a151
https://aaltodoc.aalto.fi/handle/123456789/102233
https://aaltodoc.aalto.fi/handle/123456789/102233
Autor:
Simo Särkkä, Toni Karvonen
Publikováno v:
BIT Numerical Mathematics. 59:877-902
This article derives an accurate, explicit, and numerically stable approximation to the kernel quadrature weights in one dimension and on tensor product grids when the kernel and integration measure are Gaussian. The approximation is based on use of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d32f55d8f18680be3a1e46f84a23cf71
https://doi.org/10.1007/s10543-019-00758-3
https://doi.org/10.1007/s10543-019-00758-3
Publikováno v:
IEEE Signal Processing Letters. 26:352-356
In this letter, we analyze certain student's $t$ -filters for linear Gaussian systems with misspecified noise covariances. It is shown that under appropriate conditions, the filter both estimates the state and re-scales the noise covariance matrices
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::efed9f9c05e35fd8d3d7d9f55c198c00
https://doi.org/10.1109/lsp.2018.2889440
https://doi.org/10.1109/lsp.2018.2889440
The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF. The classical quadrature rules used in the sigma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::58b1642d1f01f0ec5f1c6a908dcf349f
http://hdl.handle.net/11025/45596
http://hdl.handle.net/11025/45596
Publikováno v:
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, 58, pp.2023-2049. ⟨10.1137/19m1285974⟩
SIAM Journal on Control and Optimization, 2020, 58, pp.2023-2049. ⟨10.1137/19m1285974⟩
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, 58, pp.2023-2049. ⟨10.1137/19m1285974⟩
SIAM Journal on Control and Optimization, 2020, 58, pp.2023-2049. ⟨10.1137/19m1285974⟩
International audience; This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous-and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::672c28fdd1996158dfe2e1b1cf2d8ecc
https://hal.inria.fr/hal-03033016
https://hal.inria.fr/hal-03033016
Autor:
Toni Karvonen, Simo Särkkä
Publikováno v:
SIAM JOURNAL ON SCIENTIFIC COMPUTING. 40(2):A697-A720
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs to be sol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6b0687ef91815af0dfddc4777f750ca
http://juuli.fi/Record/0287453218
http://juuli.fi/Record/0287453218
In this paper we analyze a greedy procedure to approximate a linear functional defined in a reproducing kernel Hilbert space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals. For a large class of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23b08fe7b8388579938f4656e7a0d2d4