We consider the problem of learning from data corrupted by underrepresentation bias, where positive examples are filtered from the data at different, unknown rates for a fixed number of sensitive groups. We show that with a small amount of unbiased data, we can efficiently estimate the group-wise drop-out rates, even in settings where intersectional group membership makes learning each intersectional rate computationally infeasible. Using these estimates, we construct a reweighting scheme that allows us to approximate the loss of any hypothesis on the true distribution, even if we only observe the empirical error on a biased sample. From this, we present an algorithm encapsulating this learning and reweighting process along with a thorough empirical investigation. Finally, we define a bespoke notion of PAC learnability for the underrepresentation and intersectional bias setting and show that our algorithm permits efficient learning for model classes of finite VC dimension.
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