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Similarity functions measure how comparable pairs of elements are, and play akey role in a wide variety of applications, e.g., notions of IndividualFairness abiding by the seminal paradigm of Dwork et al., as well as Clusteringproblems. However, access to an accurate similarity function should not alwaysbe considered guaranteed, and this point was even raised by Dwork et al. Forinstance, it is reasonable to assume that when the elements to be compared areproduced by different distributions, or in other words belong to different``demographic'' groups, knowledge of their true similarity might be verydifficult to obtain. In this work, we present an efficient sampling frameworkthat learns these across-groups similarity functions, using only a limitedamount of experts' feedback. We show analytical results with rigoroustheoretical bounds, and empirically validate our algorithms via a large suiteof experiments.

Comparing Apples to Oranges: Learning Similarity Functions for Data Produced by Different Distributions