  It is a common practice in the machine learning community to assume that the
observed data are noise-free in the input attributes. Nevertheless, scenarios
with input noise are common in real problems, as measurements are never
perfectly accurate. If this input noise is not taken into account, a supervised
machine learning method is expected to perform sub-optimally. In this paper, we
focus on multi-class classification problems and use Gaussian processes (GPs)
as the underlying classifier. Motivated by a data set coming from the
astrophysics domain, we hypothesize that the observed data may contain noise in
the inputs. Therefore, we devise several multi-class GP classifiers that can
account for input noise. Such classifiers can be efficiently trained using
variational inference to approximate the posterior distribution of the latent
variables of the model. Moreover, in some situations, the amount of noise can
be known before-hand. If this is the case, it can be readily introduced in the
proposed methods. This prior information is expected to lead to better
performance results. We have evaluated the proposed methods by carrying out
several experiments, involving synthetic and real data. These include several
data sets from the UCI repository, the MNIST data set and a data set coming
from astrophysics. The results obtained show that, although the classification
error is similar across methods, the predictive distribution of the proposed
methods is better, in terms of the test log-likelihood, than the predictive
distribution of a classifier based on GPs that ignores input noise.
