Correcting Underrepresentation and Intersectional Bias in Machine Learning

Abstract I consider the problem of learning from data corrupted by underrepresentation bias, where positive examples are filtered out at different, unknown rates for a fixed number of sensitive groups. I show that with a small amount of unbiased data, I 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, I construct a reweighting scheme that allows me to approximate the loss of any hypothesis on the true distribution and present an algorithm encapsulating this process. Finally, I define a bespoke notion of PAC learnability for the underrepresentation and intersectional bias setting and show that my algorithm allows efficient learning for model classes of finite VC dimension.