Obtaining Fairness using Optimal Transport Theory

By Paula Gordaliza, Eustasio del Barrio, Fabrice Gamboa, Jean-Michel Loubes. 2018

216 citations recorded by the source corpus.

Statistical algorithms are usually helping in making decisions in many aspects of our lives. But, how do we know if these algorithms are biased and commit unfair discrimination of a particular group of people, typically a minority? \textit{Fairness} is generally studied in a probabilistic framework where it is assumed that there exists a protected variable, whose use as an input of the algorithm may imply discrimination. There are different definitions of Fairness in the literature. In this paper we focus on two of them which are called Disparate Impact (DI) and Balanced Error Rate (BER). Both are based on the outcome of the algorithm across the different groups determined by the protected variable. The relationship between these two notions is also studied. The goals of this paper are to detect when a binary classification rule lacks fairness and to try to fight against the potential discrimination attributable to it. This can be done by modifying either the classifiers or the data itself. Our work falls into the second category and modifies the input data using optimal transport theory.

Subfields: Economics and Econometrics

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In Economics and Econometrics

1. Larry A. Wasserman
2. Aldo Pacchiano
3. Sivaraman Balakrishnan
4. Heinrich Jiang
5. Silvia Chiappa

Citations in the corpus

• Wasserstein Fair Classification (2019, background): “Lemma 4 extends this simple case to the general case of datasets of arbitrary orderings and sizes, see Deshpande et al. (2018) for a proof.”
• A General Approach to Fairness with Optimal Transport (2020, background): “There has been an increasing interest in the use of optimal transport for fairness (Black, Yeom, and Fredrikson 2019; Del Barrio et al. 2019; Jiang et al. 2019; Johndrow and Lum 2019; Risser et al. 2019; Wang, Ustun, and Calmon 2019).”
• Noise-tolerant fair classification (2019, methodology): “…three main categories: — pre-processing methods (Zemel et al., 2013; Louizos et al., 2015; Lum & Johndrow, 2016; Johndrow & Lum, 2017; Calmon et al., 2017; del Barrio et al., 2018; Adler et al., 2018), which usually embed the representation of data into a new space such that the bias is removed.”
• Fairness risk measures (2019, background): “…the training set to ensure fairness of any learned model [Zemel et al., 2013, Johndrow and Lum, 2017, Calmon et al., 2017, Adler et al., 2018, del Barrio et al., 2018, McNamara et al., 2019]; ( b ) post-process model predictions to ensure their fairness [Feldman et al., 2015, Hardt et al.,…”
• Plugin estimation of smooth optimal transport maps (2021, background): “…regression (Ghodrati and Panaretos, 2021), generative modeling (Finlay et al., 2020; Onken et al., 2021), fairness in machine learning (Gordaliza et al., 2019; Black et al., 2020; de Lara et al., 2021), and in a wide range of statistical applications to the sciences (Read, 1999; Wang…”