Predictive Active Set Selection Methods for Gaussian Processes

TL;DR

This paper introduces an active set selection framework for Gaussian process classification that efficiently handles large datasets by iteratively updating the active set based on predictive distribution contributions, balancing interpretability and computational complexity.

Contribution

It presents a novel active set selection method for Gaussian processes that improves scalability and maintains accuracy, supported by theoretical and empirical evidence.

Findings

Competitive classification performance with large datasets

Effective active set update rules based on predictive contributions

Balance between interpretability and computational efficiency

Abstract

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization. The active set update rules rely on the ability of the predictive distributions of a Gaussian process classifier to estimate the relative contribution of a datapoint when being either included or removed from the model. This means that we can use it to include points with potentially high impact to the classifier decision process while removing those that are less relevant. We introduce two active set rules based on different criteria, the first one prefers a model with interpretable active set parameters whereas the second puts computational complexity first, thus a model with active set parameters that directly control its complexity. We also provide both theoretical and empirical support for our active set selection strategy being a good approximation of a full Gaussian process classifier. Our extensive experiments show that our approach can compete with state-of-the-art classification techniques with reasonable time complexity. Source code publicly available at http://cogsys.imm.dtu.dk/passgp.