We consider the problem of learning accurate models from multiple sources of "nearby" data. Given distinct samples from multiple data sources and estimates of the dissimilarities between these sources, we provide a general theory of which samples should be used to learn models for each source. This theory is applicable in a broad decision-theoretic learning framework, and yields general results for classification and regression. A key component of our approach is the development of approximate triangle inequalities for expected loss, which may be of independent interest. We discuss the related problem of learning parameters of a distribution from multiple data sources. Finally, we illustrate our theory through a series of synthetic simulations.