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。

公平分类：纠正样本差异和交叉偏见

Correcting Underrepresentation and Intersectional Bias for Fair  Classification

With the rapid increase of large-scale, real-world datasets, it becomes
critical to address the problem of long-tailed data distribution (i.e., a few
classes account for most of the data, while most classes are
under-represented). Existing solutions typically adopt class re-balancing
strategies such as re-sampling and re-weighting based on the number of
observations for each class. In this work, we argue that as the number of
samples increases, the additional benefit of a newly added data point will
diminish. We introduce a novel theoretical framework to measure data overlap by
associating with each sample a small neighboring region rather than a single
point. The effective number of samples is defined as the volume of samples and
can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is
the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a
re-weighting scheme that uses the effective number of samples for each class to
re-balance the loss, thereby yielding a class-balanced loss. Comprehensive
experiments are conducted on artificially induced long-tailed CIFAR datasets
and large-scale datasets including ImageNet and iNaturalist. Our results show
that when trained with the proposed class-balanced loss, the network is able to
achieve significant performance gains on long-tailed datasets.

研究长尾数据在机器学习任务中的问题，并提出了使用 “有效样本数” 改进重新权重计算的类平衡损失方法来提高对长尾数据集的训练效果。在人工合成的长尾 CIFAR 数据集和大规模数据集 ImageNet 和 iNaturalist 上进行了全面的实验，并证明该方法能够显著提高长尾数据集上的网络表现。