Splitting Gaussian Process Regression for Streaming Data

TL;DR

This paper introduces a novel local Gaussian process regression method designed for streaming data, significantly improving scalability by partitioning input space and maintaining linear memory complexity.

Contribution

The paper presents a new sequential partitioning algorithm for Gaussian processes that achieves linear memory use and better time complexity, suitable for streaming data applications.

Findings

Outperforms existing methods in time and space complexity

Achieves linear memory complexity for local Gaussian process models

Proven theoretical continuity properties of the model

Abstract

Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In particular, the cubic time complexity of updating standard Gaussian process models make them generally unsuitable for application to streaming data. We propose an algorithm for sequentially partitioning the input space and fitting a localized Gaussian process to each disjoint region. The algorithm is shown to have superior time and space complexity to existing methods, and its sequential nature permits application to streaming data. The algorithm constructs a model for which the time complexity of updating is tightly bounded above by a pre-specified parameter. To the best of our knowledge, the model is the first local Gaussian process regression model to achieve linear memory complexity. Theoretical continuity properties of the model are proven. We demonstrate the efficacy of the resulting model on multi-dimensional regression tasks for streaming data.