Reducing hidden bias in the data and ensuring fairness in algorithmic data
analysis has recently received significant attention. We complement several
recent papers in this line of research by introducing a general method to
reduce bias in the data through random projections in a "fair" subspace.
We apply this method to densest subgraph problem. For densest subgraph, our
approach based on fair projections allows to recover both theoretically and
empirically an almost optimal, fair, dense subgraph hidden in the input data.
We also show that, under the small set expansion hypothesis, approximating this
problem beyond a factor of 2 is NP-hard and we show a polynomial time algorithm
with a matching approximation bound.

在算法数据分析中，通过随机投影到 “公平” 子空间来减少数据中的偏差，我们将这种方法应用于最密子图问题，理论上和实验上都可以恢复一个几乎最优、公平、稠密的子图，并通过匹配逼近上界展示该问题的 NP - 难度特性。

通过投影消除偏差的主要公平性

Principal Fairness: Removing Bias via Projections

The quality of training data is one of the crucial problems when a
learning-centered approach is employed. This paper proposes a new method to
investigate the quality of a large corpus designed for the recognizing textual
entailment (RTE) task. The proposed method, which is inspired by a statistical
hypothesis test, consists of two phases: the first phase is to introduce the
predictability of textual entailment labels as a null hypothesis which is
extremely unacceptable if a target corpus has no hidden bias, and the second
phase is to test the null hypothesis using a Naive Bayes model. The
experimental result of the Stanford Natural Language Inference (SNLI) corpus
does not reject the null hypothesis. Therefore, it indicates that the SNLI
corpus has a hidden bias which allows prediction of textual entailment labels
from hypothesis sentences even if no context information is given by a premise
sentence. This paper also presents the performance impact of NN models for RTE
caused by this hidden bias.

本文提出了一种新的方法来研究用于识别文本蕴含任务的大型语料库的质量，通过基于统计假设检验的方法，测试了斯坦福自然语言推理（SNLI）语料库的可预测性，结果表明该库存在隐藏的偏差，并呈现了此偏差对于 RTE 的 NN 模型性能的影响。