detalle del documento
IDENTIFICACIÓN
oai:arXiv.org:2409.14585
Tema
Mathematics - Numerical Analysis Mathematics - Probability Statistics - Computation Statistics - Machine Learning 60G25, 60G35, 62F15, 62G07, 62M20,...Autor
Bågmark, Kasper Andersson, Adam Larsson, Stig Rydin, FilipCategoría
Computer Science
Año
2024
fecha de cotización
22/1/2025
Palabras clave
equation fokker--planck numerical schemeResumen
A numerical scheme for approximating the nonlinear filtering density is introduced and its convergence rate is established, theoretically under a parabolic H\"ormander condition, and empirically in two numerical examples.
For the prediction step, between the noisy and partial measurements at discrete times, the scheme approximates the Fokker--Planck equation with a deep splitting scheme, combined with an exact update through Bayes' formula.
This results in a classical prediction-update filtering algorithm that operates online for new observation sequences post-training.
The algorithm employs a sampling-based Feynman--Kac approach, designed to mitigate the curse of dimensionality.
The convergence proof relies on stochastic integration by parts from the Malliavin calculus.
As a corollary we obtain the convergence rate for the approximation of the Fokker--Planck equation alone, disconnected from the filtering problem.
;Comment: 25 pages, 2 figures
Bågmark, Kasper,Andersson, Adam,Larsson, Stig,Rydin, Filip, 2024, A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting
Evaluating Image Hallucination in Text-to-Image Generation with Question-Answering
evaluation computer dataset images tti generation i-halla
Role of Repetitive Transcranial Magnetic Stimulation in Treatment of Fibromyalgia: A Randomized Controlled Trial
significant following stimulation fms treatment
