Ensemble Kalman Filtering for Online Gaussian Process Regression and Learning
This work addresses the challenge of real-time and sequential data processing for Gaussian processes, which is incremental as it builds on existing inducing point methods.
The paper tackles the high computational complexity of Gaussian process regression for online tasks by proposing a novel online algorithm using ensemble Kalman filtering to train sparse models, achieving reduced computational complexity while maintaining prediction accuracy on synthetic and real-world datasets like UK house prices.
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.