Fair Principal Component Analysis (PCA) is a problem setting where we aim to
perform PCA while making the resulting representation fair in that the
projected distributions, conditional on the sensitive attributes, match one
another. However, existing approaches to fair PCA have two main problems:
theoretically, there has been no statistical foundation of fair PCA in terms of
learnability; practically, limited memory prevents us from using existing
approaches, as they explicitly rely on full access to the entire data. On the
theoretical side, we rigorously formulate fair PCA using a new notion called
\emph{probably approximately fair and optimal} (PAFO) learnability. On the
practical side, motivated by recent advances in streaming algorithms for
addressing memory limitation, we propose a new setting called \emph{fair
streaming PCA} along with a memory-efficient algorithm, fair noisy power method
(FNPM). We then provide its {\it statistical} guarantee in terms of
PAFO-learnability, which is the first of its kind in fair PCA literature.
Lastly, we verify the efficacy and memory efficiency of our algorithm on
real-world datasets.

公平主成分分析（Fair Principal Component Analysis，fair PCA）是一个问题设置，旨在在执行主成分分析的同时，使得所得到的表示在条件敏感属性的情况下相互匹配的分布公平。然而，现有的公平主成分分析方法存在两个主要问题：从理论上讲，公平主成分分析在可学习性方面没有统计学基础；从实际上讲，有限的内存限制了现有方法的使用，因为它们明确要求对所有数据进行完全访问。在理论上，我们使用一个称为 “可能近似公平和最优学习”（PAFO-learnability）的新概念，严格地制定了公平主成分分析。在实际上，受近期应对内存限制的流数据算法的最新进展的启发，我们提出了一种称为 “公平流式主成分分析（fair streaming PCA）” 的新设置，以及一种内存高效的算法，公平噪声幂法（fair noisy power method，FNPM）。然后，在公平主成分分析文献中，我们提供了该算法的统计保证，这是其首次存在。最后，我们验证了我们算法在现实世界数据集上的效果和内存效率。

公平的流式主成分分析：统计和算法视角

Fair Streaming Principal Component Analysis: Statistical and Algorithmic  Viewpoint

We propose a novel taxonomy for bias evaluation of discriminative foundation
models, such as Contrastive Language-Pretraining (CLIP), that are used for
labeling tasks. We then systematically evaluate existing methods for mitigating
bias in these models with respect to our taxonomy. Specifically, we evaluate
OpenAI's CLIP and OpenCLIP models for key applications, such as zero-shot
classification, image retrieval and image captioning. We categorize desired
behaviors based around three axes: (i) if the task concerns humans; (ii) how
subjective the task is (i.e., how likely it is that people from a diverse range
of backgrounds would agree on a labeling); and (iii) the intended purpose of
the task and if fairness is better served by impartiality (i.e., making
decisions independent of the protected attributes) or representation (i.e.,
making decisions to maximize diversity). Finally, we provide quantitative
fairness evaluations for both binary-valued and multi-valued protected
attributes over ten diverse datasets. We find that fair PCA, a post-processing
method for fair representations, works very well for debiasing in most of the
aforementioned tasks while incurring only minor loss of performance. However,
different debiasing approaches vary in their effectiveness depending on the
task. Hence, one should choose the debiasing approach depending on the specific
use case.

我们提出了一种用于评估具有歧视性基础模型（如相互对比语言预训练模型）的偏差的新分类方法，并根据该分类方法系统评估了现有的缓解这些模型偏差的方法。我们针对 OpenAI 的 CLIP 和 OpenCLIP 模型对关键的应用进行了评估，例如零样本分类、图像检索和图像字幕等。我们根据三个方面对所需的行为进行了分类：（i）任务是否涉及人类；（ii）任务的主观性程度（即，不同背景的人们是否会同意标注）；以及（iii）任务的预期目的，是否通过公正性（即，独立于受保护属性进行决策）或代表性（即，通过最大程度地增加多样性进行决策）来更好地服务于公平性。最后，我们在十个不同的数据集上提供了二元和多值受保护属性的定量公平性评估结果。我们发现，用于公平性表示的后处理方法 “公平 PCA” 在大多数上述任务的去偏中效果非常好，同时只带来了轻微的性能损失。然而，不同的去偏方法在不同的任务中的有效性有所不同。因此，对于特定的使用情况，应选择相应的去偏方法。