Variable selection for Gaussian processes via sensitivity analysis of the posterior predictive distribution

TL;DR

This paper introduces two new variable selection methods for Gaussian process models that leverage local predictive analysis, outperforming traditional relevance determination in accuracy and stability.

Contribution

The authors propose novel variable selection techniques based on sensitivity analysis of the posterior predictive distribution, enhancing predictive accuracy over existing methods.

Findings

Improved variable selection accuracy on synthetic data.

Enhanced predictive performance on real-world datasets.

Greater stability in variable relevance ranking.

Abstract

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined relevance has several drawbacks that prevent the selection of optimal input variables in terms of predictive performance. To improve on this, we propose two novel variable selection methods for Gaussian process models that utilize the predictions of a full model in the vicinity of the training points and thereby rank the variables based on their predictive relevance. Our empirical results on synthetic and real world data sets demonstrate improved variable selection compared to automatic relevance determination in terms of variability and predictive performance.