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Limitations of Pinned AUC for Measuring Unintended Bias

Daniel Borkan, Lucas Dixon, John Li, Jeffrey Sorensen, Nithum Thain, Lucy Vasserman

arXiv:1903.02088v1stat.MLcs.LG

TL;DR

Pinned AUC is a threshold-agnostic measure of unintended bias, but its measurements can be skewed when class distributions vary across identities. This report demonstrates that limitation and decomposes the metric into alternatives presented in [1], which it describes as robust to distribution changes and more nuanced.

  • Problem

    The report examines whether Pinned AUC can measure unintended bias reliably when classification-label distributions differ across identities.

    Source: §1 · p. 1

  • Method

    The report demonstrates how class-distribution differences affect Pinned AUC and decomposes the metric into the threshold-agnostic metrics presented in [1].

    Source: §1 · p. 1, §2.3 · p. 2

  • Results

    Pinned AUC can report reduced or increased bias when subgroup class balance changes despite the same underlying bias, including a TOXICITY@1 change from 0.87 to 0.91 for “gay” in the skewed test set.

    Source: §2.2 · p. 2, §3.3 · p. 4

  • Takeaways & Limitations

    The metrics presented in [1] are described as robust to distribution changes and as providing a more nuanced view of unintended bias than Pinned AUC.

    Source: §4 · p. 4

    Pinned AUC's requirement for perfectly balanced test sets limits its use on realistic datasets, where class balance rarely matches across demographic subgroups.

    Source: §2.2 · p. 2

Abstract

from arXiv · show

This report examines the Pinned AUC metric introduced and highlights some of its limitations. Pinned AUC provides a threshold-agnostic measure of unintended bias in a classification model, inspired by the ROC-AUC metric. However, as we highlight in this report, there are ways that the metric can obscure different kinds of unintended biases when the underlying class distributions on which bias is being measured are not carefully controlled.

1 Introduction

The report examines Pinned AUC as a threshold-agnostic measure of unintended bias and explains how uncontrolled class distributions can skew its measurements. It also presents metrics from [1] as a more robust, nuanced alternative that avoids requiring careful class balancing.

1 Introduction

  • Pinned AUC can overstate or understate unintended bias when class distributions differ across identities.The metric avoids this potential distortion when identity subgroups have identical representation of classification labels.Source: §1 · p. 1
  • The report demonstrates why Pinned AUC is not robust to variations in class distributions.Source: §1 · p. 1
  • The report shows how Pinned AUC can be decomposed into the threshold-agnostic metrics presented in [1].Those metrics are described as robust to distribution changes and as providing a more nuanced view of unintended bias.Source: §1 · p. 1

2 Pinned AUC Limitations

Pinned AUC measures subgroup model quality within a background distribution, but its value can be distorted when class balance varies across identity subgroups. The report shows that the metric’s pair-count weighting explains this distortion and limits its applicability to perfectly balanced datasets.

2.1 Pinned AUC Summary

  • Pinned AUC calculates ROC-AUC on a pinned dataset containing 50% subgroup examples and 50% randomly sampled examples from the background dataset.It measures the subgroup in the context of a general background distribution.Source: §2.1 · p. 1

2.2 Restriction on Pinned AUC

  • A subgroup score shift can make its non-toxic examples score like background toxic examples, preventing a single threshold; Table 1’s example has Pinned AUC 0.94.The table presents hypothetical score distributions, with non-toxic examples in red and toxic examples in blue.Source: §2.2 · pp. 1–2, Table 1 · p. 2
  • Different subgroup class balances make Pinned AUC report different bias levels even when score distributions—and the extent of unintended bias—are unchanged.The report concludes that this distortion makes Pinned AUC applicable only to perfectly balanced datasets.Source: §2.2 · p. 2, Table 1 · p. 2
  • Pinned AUC’s balanced-set assumption limits its value on realistic data: synthetic data can be balanced but offers a limited view, while real demographic subgroups rarely have equal class balance.The report notes that realistic synthetic data with broad coverage is challenging to create.Source: §2.2 · p. 2

2.3 Decomposing Pinned AUC

  • The decomposition expresses Pinned AUC as a weighted average of four AUC measures, with each weight determined by the proportion of example pairs in that group.If the numbers of examples in those pair groups vary, the overall Pinned AUC can vary as well.Source: §2.3 · p. 3

3 Experimental Results

The report tests whether skewing class balance for one identity term distorts Pinned AUC despite unchanged models and bias. On the skewed “gay” set, TOXICITY@1’s score rises from 0.87 to 0.91, seemingly erasing some bias.

3.1 Models

  • The comparison evaluates Perspective API’s initial TOXICITY@1 and latest TOXICITY@6; because TOXICITY@6 underwent bias-mitigation techniques, reduced unintended bias is expected between models as measured by Pinned AUC.TOXICITY@1 had previously shown significant unintended bias around identity words like "gay" and "transgender".Source: §3.1 · p. 3

3.2 Synthetic Test Set

  • The experiment compares TOXICITY@1 and TOXICITY@6 on an original balanced synthetic set and a version with fewer non-toxic “gay” examples.The original set has 77k template-generated examples across 50 identity terms; the skewed version removes half of the non-toxic “gay” examples, leaving 1,136 examples for that term, 66% toxic.Source: §3.2 · pp. 3–4

3.3 Synthetic Test Set Results

  • The analysis focuses on 14 identity terms whose original Pinned AUC differences between the models exceeded 0.2.It compares results on the evenly balanced and artificially skewed test sets.Source: §3.3 · p. 4
  • 0.87 to 0.91: TOXICITY@1’s Pinned AUC rises for “gay” after skewing, despite unchanged models and true bias.The effect is also present, but less strong, for TOXICITY@6.Source: §3.3 · p. 4, Table 2 · p. 4

4 Conclusion

Pinned AUC can obscure unintended bias when identity subgroups have unequal class distributions; decomposed threshold-agnostic metrics are robust to distribution changes and offer a more detailed view.

  • Pinned AUC is ineffective at measuring bias when test data has unequal class distributions across identities.Source: §4 · p. 4
  • Pinned AUC can be decomposed into threshold-agnostic metrics that remain robust to changes in data distributions.Source: §4 · p. 4
  • The decomposed metrics provide a more detailed view of unintended bias and can serve as a more general measurement framework.Source: §4 · p. 4

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