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.
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