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 parameters, even in settings where intersectional group
membership makes learning each intersectional rate computationally infeasible.
Using this estimate for the group-wise drop-out rate, we construct a
re-weighting 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. Finally, we present an algorithm encapsulating this learning and
re-weighting process, and we provide strong PAC-style guarantees that, with
high probability, our estimate of the risk of the hypothesis over the true
distribution will be arbitrarily close to the true risk.

研究了在存在样本筛选偏差的情况下，通过一种小样本无偏估计方法和重新加权方案，来有效评估基于真实分布的假设的风险，以及解决交叉组成员计算困难的问题。