The vast majority of techniques to train fair models require access to the
protected attribute (e.g., race, gender), either at train time or in
production. However, in many important applications this protected attribute is
largely unavailable. In this paper, we develop methods for measuring and
reducing fairness violations in a setting with limited access to protected
attribute labels. Specifically, we assume access to protected attribute labels
on a small subset of the dataset of interest, but only probabilistic estimates
of protected attribute labels (e.g., via Bayesian Improved Surname Geocoding)
for the rest of the dataset. With this setting in mind, we propose a method to
estimate bounds on common fairness metrics for an existing model, as well as a
method for training a model to limit fairness violations by solving a
constrained non-convex optimization problem. Unlike similar existing
approaches, our methods take advantage of contextual information --
specifically, the relationships between a model's predictions and the
probabilistic prediction of protected attributes, given the true protected
attribute, and vice versa -- to provide tighter bounds on the true disparity.
We provide an empirical illustration of our methods using voting data. First,
we show our measurement method can bound the true disparity up to 5.5x tighter
than previous methods in these applications. Then, we demonstrate that our
training technique effectively reduces disparity while incurring lesser
fairness-accuracy trade-offs than other fair optimization methods with limited
access to protected attributes.

在有限的受保护属性标签访问情况下，本文开发了测量和减少公平违规的方法，提出了估计现有模型的常见公平度量和解决约束非凸优化问题以限制公平违规的模型训练技术，并且相比其他受限受保护属性的公平优化方法，在减小公平度的同时减少了公平性和准确性的权衡。

利用概率受保护特征估计和实现常规公平度量

Estimating and Implementing Conventional Fairness Metrics With  Probabilistic Protected Features

Rotation Averaging is a non-convex optimization problem that determines
orientations of a collection of cameras from their images of a 3D scene. The
problem has been studied using a variety of distances and robustifiers. The
intrinsic (or geodesic) distance on SO(3) is geometrically meaningful; but
while some extrinsic distance-based solvers admit (conditional) guarantees of
correctness, no comparable results have been found under the intrinsic metric.
In this paper, we study the spatial distribution of local minima. First, we
do a novel empirical study to demonstrate sharp transitions in qualitative
behavior: as problems become noisier, they transition from a single
(easy-to-find) dominant minimum to a cost surface filled with minima. In the
second part of this paper we derive a theoretical bound for when this
transition occurs. This is an extension of the results of [24], which used
local convexity as a proxy to study the difficulty of problem. By recognizing
the underlying quotient manifold geometry of the problem we achieve an n-fold
improvement over prior work. Incidentally, our analysis also extends the prior
$l_2$ work to general $l_p$ costs. Our results suggest using algebraic
connectivity as an indicator of problem difficulty.

本文研究的问题是通过相机拍摄的三维场景图像确定相机方向的非凸优化问题，主要关注旋转平均的空间分布和局部极小值以及使用代数连通性作为问题难度的指标。