  Machine learning techniques have been successfully used to classify variable
stars on widely-studied astronomical surveys. These datasets have been
available to astronomers long enough, thus allowing them to perform deep
analysis over several variable sources and generating useful catalogs with
identified variable stars. The products of these studies are labeled data that
enable supervised learning models to be trained successfully. However, when
these models are blindly applied to data from new sky surveys their performance
drops significantly. Furthermore, unlabeled data becomes available at a much
higher rate than its labeled counterpart, since labeling is a manual and
time-consuming effort. Domain adaptation techniques aim to learn from a domain
where labeled data is available, the \textit{source domain}, and through some
adaptation perform well on a different domain, the \textit{target domain}. We
propose a full probabilistic model that represents the joint distribution of
features from two surveys as well as a probabilistic transformation of the
features between one survey to the other. This allows us to transfer labeled
data to a study where it is not available and to effectively run a variable
star classification model in a new survey. Our model represents the features of
each domain as a Gaussian mixture and models the transformation as a
translation, rotation and scaling of each separate component. We perform tests
using three different variability catalogs: EROS, MACHO, and HiTS, presenting
differences among them, such as the amount of observations per star, cadence,
observational time and optical bands observed, among others.
