  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.
