TITLE:
Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models
AUTHORS:
Qianli Di
KEYWORDS:
Latent Force Model, COVID-19, Quasi-Monte Carlo Approximations
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.10 No.4,
October
13,
2022
ABSTRACT: In this project, we consider obtaining Fourier
features via more efficient sampling schemes to approximate the kernel in LFMs.
A latent force model (LFM) is a Gaussian process whose covariance functions follow an
Exponentiated Quadratic (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 (RFF) are 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 (QMC) method. The first-order and second-order
models’ experiment results demonstrate the decrease in NLPD and NMSE, which
revealed that the models with QMC approximation have better performance.