%0 Journal Article
%T Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models
%A Qianli Di
%J Open Journal of Modelling and Simulation
%P 349-390
%@ 2327-4026
%D 2022
%I Scientific Research Publishing
%R 10.4236/ojmsi.2022.104021
%X <span style=\"font-family:Verdana;\">In this project, we consider obtaining Fourier
features via more efficient sampling schemes to approximate the kernel in LFMs.
A latent force model</span><span><span style=\"font-family:&quot;\"> </span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">(LFM) is a Gaussian process whose covariance functions follow an
Exponentiated Quadratic</span></span><span><span style=\"font-family:&quot;\"> </span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">(EQ) form, and the solutions for the cross-covariance are expensive due
to the computational complexity. To reduce the complexity of mathematical
expressions, random Fourier features</span></span><span><span style=\"font-family:&quot;\"> </span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">(RFF) </span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">are</span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> applied to approximate the EQ kernel. Usually, the
random Fourier features are implemented with Monte Carlo sampling, but this
project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo</span></span><span><span style=\"font-family:&quot;\"> </span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">(QMC) method. The first-order and second-order
modelsĄŻ experiment results demonstrate the decrease in NLPD and NMSE, which
revealed that the models with QMC approximation have better performance.
%K Latent Force Model
%K COVID-19
%K Quasi-Monte Carlo Approximations
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=120387