Accurately measuring discrimination in machine learning-based automated
decision systems is required to address the vital issue of fairness between
subpopulations and/or individuals. Any bias in measuring discrimination can
lead to either amplification or underestimation of the true value of
discrimination. This paper focuses on a class of bias originating in the way
training data is generated and/or collected. We call such class causal biases
and use tools from the field of causality to formally define and analyze such
biases. Four sources of bias are considered, namely, confounding, selection,
measurement, and interaction. The main contribution of this paper is to
provide, for each source of bias, a closed-form expression in terms of the
model parameters. This makes it possible to analyze the behavior of each source
of bias, in particular, in which cases they are absent and in which other cases
they are maximized. We hope that the provided characterizations help the
community better understand the sources of bias in machine learning
applications.

准确测量在基于机器学习的自动决策系统中的歧视是解决子群体和 / 或个体间公平性的重要问题所必需的。本文关注于在生成和 / 或收集训练数据的方式中出现的一类偏见，我们称之为因果偏见，并使用因果关系领域的工具来正式定义和分析此类偏见。本文考虑了四种来源的偏见，即混杂、选择、测量和交互。本文的主要贡献是为每种偏见提供了一个基于模型参数的闭合表达式。这使得分析每种偏见的行为成为可能，特别是在哪些情况下它们不存在，以及在哪些其他情况下它们被最大化。我们希望提供的特征有助于社会更好地理解机器学习应用中偏见的来源。