A Scalable Gaussian Process for Large-Scale Periodic Data

01/04/2023
βˆ™
by   Yongxiang Li, et al.
βˆ™
0
βˆ™

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 π’ͺ(n^3) (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 π’ͺ(p^2) (or π’ͺ(plog p) 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.

READ FULL TEXT

page 23

page 28

page 29

page 30

research
βˆ™ 12/09/2014

Hierarchical Mixture-of-Experts Model for Large-Scale Gaussian Process Regression

We propose a practical and scalable Gaussian process model for large-sca...
research
βˆ™ 11/30/2017

Nonseparable Gaussian Stochastic Process: A Unified View and Computational Strategy

Gaussian stochastic process (GaSP) has been widely used as a prior over ...
research
βˆ™ 06/24/2020

Likelihood-Free Gaussian Process for Regression

Gaussian process regression can flexibly represent the posterior distrib...
research
βˆ™ 09/29/2020

Robust Detection of Objects under Periodic Motion with Gaussian Process Filtering

Object Detection (OD) is an important task in Computer Vision with many ...
research
βˆ™ 09/20/2021

Barely Biased Learning for Gaussian Process Regression

Recent work in scalable approximate Gaussian process regression has disc...
research
βˆ™ 05/30/2021

Periodic-GP: Learning Periodic World with Gaussian Process Bandits

We consider the sequential decision optimization on the periodic environ...
research
βˆ™ 02/25/2022

Scalable Gaussian-process regression and variable selection using Vecchia approximations

Gaussian process (GP) regression is a flexible, nonparametric approach t...

Please sign up or login with your details

Forgot password? Click here to reset