  Gaussian processes (GP) are attractive building blocks for many probabilistic
models. Their drawbacks, however, are the rapidly increasing inference time and
memory requirement alongside increasing data. The problem can be alleviated
with compactly supported (CS) covariance functions, which produce sparse
covariance matrices that are fast in computations and cheap to store. CS
functions have previously been used in GP regression but here the focus is in a
classification problem. This brings new challenges since the posterior
inference has to be done approximately. We utilize the expectation propagation
algorithm and show how its standard implementation has to be modified to obtain
computational benefits from the sparse covariance matrices. We study four CS
covariance functions and show that they may lead to substantial speed up in the
inference time compared to globally supported functions.
