{"title":"Fair Data Representation for Machine Learning at the Pareto Frontier.","authors":"Shizhou Xu, Thomas Strohmer","doi":"","DOIUrl":null,"url":null,"abstract":"<p><p>As machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness in the underlying data processing. We propose a pre-processing algorithm for fair data representation via which <math> <mrow><msup><mi>L</mi> <mn>2</mn></msup> <mo>(</mo> <mtext>ℙ</mtext> <mo>)</mo></mrow> </math> -objective supervised learning results in estimations of the Pareto frontier between prediction error and statistical disparity. Particularly, the present work applies the optimal affine transport to approach the post-processing Wasserstein barycenter characterization of the optimal fair <math> <mrow><msup><mi>L</mi> <mn>2</mn></msup> </mrow> </math> -objective supervised learning via a pre-processing data deformation. Furthermore, we show that the Wasserstein geodesics from learning outcome marginals to their barycenter characterizes the Pareto frontier between <math> <mrow><msup><mi>L</mi> <mn>2</mn></msup> </mrow> </math> -loss and total Wasserstein distance among the marginals. Numerical simulations underscore the advantages: (1) the pre-processing step is compositive with arbitrary conditional expectation estimation supervised learning methods and unseen data; (2) the fair representation protects the sensitive information by limiting the inference capability of the remaining data with respect to the sensitive data; (3) the optimal affine maps are computationally efficient even for high-dimensional data.</p>","PeriodicalId":50161,"journal":{"name":"Journal of Machine Learning Research","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11494318/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Machine Learning Research","FirstCategoryId":"94","ListUrlMain":"","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
As machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness in the underlying data processing. We propose a pre-processing algorithm for fair data representation via which -objective supervised learning results in estimations of the Pareto frontier between prediction error and statistical disparity. Particularly, the present work applies the optimal affine transport to approach the post-processing Wasserstein barycenter characterization of the optimal fair -objective supervised learning via a pre-processing data deformation. Furthermore, we show that the Wasserstein geodesics from learning outcome marginals to their barycenter characterizes the Pareto frontier between -loss and total Wasserstein distance among the marginals. Numerical simulations underscore the advantages: (1) the pre-processing step is compositive with arbitrary conditional expectation estimation supervised learning methods and unseen data; (2) the fair representation protects the sensitive information by limiting the inference capability of the remaining data with respect to the sensitive data; (3) the optimal affine maps are computationally efficient even for high-dimensional data.
随着机器学习驱动的决策在我们的日常生活中变得越来越重要,在底层数据处理中力求公平势在必行。我们提出了一种用于公平数据表示的预处理算法,通过这种算法,目标监督学习可以估计预测误差和统计差异之间的帕累托前沿。特别是,本研究应用最优仿射传输,通过预处理数据变形,接近最优公平 L 2 目标监督学习的后处理 Wasserstein barycenter 特性。此外,我们还证明了从学习结果边际到其原点的瓦瑟斯坦大地线表征了边际间的 L 2 -损失和总瓦瑟斯坦距离之间的帕累托前沿。数值模拟证明了该方法的优势:(1)预处理步骤与任意条件期望估计监督学习方法和未见数据具有可比性;(2)公平表示通过限制其余数据相对于敏感数据的推理能力来保护敏感信息;(3)即使对于高维数据,最优仿射图的计算效率也很高。
期刊介绍:
The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online.
JMLR has a commitment to rigorous yet rapid reviewing.
JMLR seeks previously unpublished papers on machine learning that contain:
new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature;
experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems;
accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods;
formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks;
development of new analytical frameworks that advance theoretical studies of practical learning methods;
computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.