A Scalable Gaussian Process for Large-Scale Periodic Data

TL;DR

This paper introduces a scalable circulant Gaussian process model for large-scale periodic data, significantly reducing computational complexity and enabling applications previously hindered by high computational costs.

Contribution

The paper proposes a novel circulant PGP model that decomposes the likelihood into scalable components, allowing efficient analysis of large periodic datasets without approximations.

Findings

CPGP reduces likelihood computation to O(p^2) or O(p log p) time.

Simulations show CPGP outperforms existing methods in periodicity estimation.

Real case studies demonstrate CPGP's effectiveness on large-scale data.

Abstract

The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data size), which hinders its wide application. To address this issue, we propose a novel circulant PGP (CPGP) model for large-scale periodic data collected at grids that are commonly seen in signal processing applications. The proposed CPGP decomposes the log-likelihood of PGP into the sum of two computationally scalable composite log-likelihoods, which do not involve any approximations. Computing the likelihood of CPGP requires only $\mathcal{O}\left(p^{2}\right)$ (or $\mathcal{O}\left(p\log p\right)$ in some special cases) time for grid observations, where the segment length $p$ is independent of and much smaller than $n$. Simulations and real case studies are presented to show the superiority of CPGP over some state-of-the-art methods, especially for applications requiring periodicity estimation. This new modeling technique can greatly advance the applicability of PGP in many areas and allow the modeling of many previously intractable problems.