Ensemble Kalman Filtering for Online Gaussian Process Regression and Learning

TL;DR

This paper introduces an online ensemble Kalman filtering approach for Gaussian process regression, enabling real-time learning and prediction with reduced computational complexity while maintaining accuracy.

Contribution

The paper presents a novel online algorithm that models Gaussian process mean and hyperparameters as states and parameters of an ensemble Kalman filter, suitable for sequential data.

Findings

Effective on synthetic datasets.

Scalable to large real-world datasets.

Maintains prediction accuracy with reduced computation.

Abstract

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically with the number of observations. Several approaches based on inducing points were proposed to handle this problem in a static context. These methods though face challenges with real-time tasks and when the data is received sequentially over time. In this paper, a novel online algorithm for training sparse Gaussian process models is presented. It treats the mean and hyperparameters of the Gaussian process as the state and parameters of the ensemble Kalman filter, respectively. The online evaluation of the parameters and the state is performed on new upcoming samples of data. This procedure iteratively improves the accuracy of parameter estimates. The ensemble Kalman filter reduces the computational complexity required to obtain predictions with Gaussian processes preserving the accuracy level of these predictions. The performance of the proposed method is demonstrated on the synthetic dataset and real large dataset of UK house prices.