A structural equation formulation for general quasi-periodic Gaussian processes

TL;DR

This paper presents a new structural equation approach for quasi-periodic Gaussian processes that simplifies modeling, improves computational efficiency, and provides reliable parameter estimates for analyzing natural and physiological signals.

Contribution

It introduces a novel structural equation formulation for quasi-periodic Gaussian processes, enhancing scalability and estimation accuracy over existing methods.

Findings

Reduced likelihood evaluation cost from O(k^2 p^2) to O(p^2)

Demonstrated effectiveness on tidal, CO2, and sunspot data

Provided a bootstrap method for confidence intervals

Abstract

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO$_{2}$ emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from $\mathcal{O}(k^2 p^2)$ to $\mathcal{O}(p^2)$, significantly improving scalability.