  In this contribution we describe an approach to evolve composite covariance
functions for Gaussian processes using genetic programming. A critical aspect
of Gaussian processes and similar kernel-based models such as SVM is, that the
covariance function should be adapted to the modeled data. Frequently, the
squared exponential covariance function is used as a default. However, this can
lead to a misspecified model, which does not fit the data well. In the proposed
approach we use a grammar for the composition of covariance functions and
genetic programming to search over the space of sentences that can be derived
from the grammar. We tested the proposed approach on synthetic data from
two-dimensional test functions, and on the Mauna Loa CO2 time series. The
results show, that our approach is feasible, finding covariance functions that
perform much better than a default covariance function. For the CO2 data set a
composite covariance function is found, that matches the performance of a
hand-tuned covariance function.
