  Probabilistic classification of unassociated Fermi-LAT sources using machine
learning methods has an implicit assumption that the distributions of
associated and unassociated sources are the same as a function of source
parameters, which is not the case for the Fermi-LAT catalogs. The problem of
different distributions of training and testing (or target) datasets as a
function of input features (covariates) is known as the covariate shift. In
this paper, we, for the first time, quantitatively estimate the effect of the
covariate shift on the multi-class classification of Fermi-LAT sources. We
introduce sample weights proportional to the ratio of unassociated to
associated source probability density functions so that associated sources in
areas, which are densely populated with unassociated sources, have more weight
than the sources in areas with few unassociated sources. We find that the
covariate shift has relatively little effect on the predicted probabilities,
i.e., the training can be performed either with weighted or with unweighted
samples, which is generally expected for the covariate shift problems. The main
effect of the covariate shift is on the estimated performance of the
classification. Depending on the class, the covariate shift can lead up to 10 -
20% reduction in precision and recall compared to the estimates, where the
covariate shift is not taken into account.
