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2019 | OriginalPaper | Chapter

A Causal Bayesian Networks Viewpoint on Fairness

Authors : Silvia Chiappa, William S. Isaac

Published in: Privacy and Identity Management. Fairness, Accountability, and Transparency in the Age of Big Data

Publisher: Springer International Publishing

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Abstract

We offer a graphical interpretation of unfairness in a dataset as the presence of an unfair causal effect of the sensitive attribute in the causal Bayesian network representing the data-generation mechanism. We use this viewpoint to revisit the recent debate surrounding the COMPAS pretrial risk assessment tool and, more generally, to point out that fairness evaluation on a model requires careful considerations on the patterns of unfairness underlying the training data. We show that causal Bayesian networks provide us with a powerful tool to measure unfairness in a dataset and to design fair models in complex unfairness scenarios.

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Appendix
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Footnotes
1
Throughout the paper, we use capital and small letters for random variables and their values, and calligraphic capital letters for sets of variables.
 
2
While the exact methodology underlying GRRS and VRRS is proprietary, publicly available reports suggest that the process begins with a defendant being administered a 137 point assessment during intake. This is used to create a series of dynamic risk factor scales such as the criminal involvement scale and history of violence scale. In addition, COMPAS also includes static attributes such as the defendant’s age and prior police contact (number of prior arrests). The raw COMPAS scores are transformed into decile values by ranking and calibration with a normative group to ensure an equal proportion of scores within each scale value. Lastly, to aid practitioner interpretation, the scores are grouped into three risk categories. The scale values are displayed to court officials as either Low (1–4), Medium (5–7), and High (8–10) risk.
 
3
The equality \(p(Y_a|A=a)=p(Y|A=a)\) is called consistency.
 
4
Often the AIE of \(A=a\) with respect to \(A=\bar{a}\) is defined as \(\text {AIE}^a_{\bar{a} a} = \langle Y_{a} \rangle _{p(Y_{a})} - \langle Y_{a}(M_{\bar{a}}) \rangle _{p(Y_{a}(M_{\bar{a}}))}= -\text {AIE}_{a \bar{a} }\), which differs in setting A to a rather than to \(\bar{a}\) along \(A\rightarrow Y\). In the linear case, the two definitions coincide (see Eqs. (2) and (3)). Similarly the ADE can be defined as \(\text {ADE}^a_{\bar{a} a} = \langle Y_{a} \rangle _{p(Y_{a})} - \langle Y_{\bar{a}}(M_a) \rangle _{p(Y_{\bar{a}}(M_a))}= -\text {ADE}_{a \bar{a} }\).
 
5
Notice that https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-16744-8_1/479119_1_En_1_IEq259_HTML.gif , but https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-16744-8_1/479119_1_En_1_IEq260_HTML.gif .
 
6
Notice that https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-16744-8_1/479119_1_En_1_IEq264_HTML.gif . Indeed \(\langle Y \rangle _{p(Y|A=a, Q=q^n, D=d^n)}=\theta ^y+\theta ^y_{a}+\theta ^y_{q}q^n+\theta ^y_{d}d^n\) and \(\text {PSE}_{\bar{a} a}=\theta ^y_a\). This equivalence does not hold in the non-linear setting.
 
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Metadata
Title
A Causal Bayesian Networks Viewpoint on Fairness
Authors
Silvia Chiappa
William S. Isaac
Copyright Year
2019
Book
Privacy and Identity Management. Fairness, Accountability, and Transparency in the Age of Big Data

Print ISBN: 978-3-030-16743-1

Electronic ISBN: 978-3-030-16744-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-16744-8_1

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