arXiv 27 Jul 2022 · Statistics — Methodology
arXiv:2207.13797 · PDF · DOI · OpenAlex · Extracted main text
These notes shows how to do inference on the Demographic Parity (DP) metric. Although the metric is a complex statistic involving min and max computations, we propose a smooth approximation of those functions and derive its asymptotic distribution. The limit of these approximations and their gradients converge to those of the true max and min functions, wherever they exist. More importantly, when the true max and min functions are not differentiable, the approximations still are, and they provide valid asymptotic inference everywhere in the domain. We conclude with some directions on how to compute confidence intervals for DP, how to test if it is under 0.8 (the U.S. Equal Employment Opportunity Commission fairness threshold), and how to do inference in an A/B test.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Blanchard, P., Higham, D. J., and Higham, N. J (2019) Accurate computation of the log-sum-exp and softmax functions | 0.405 | 1 | 1 | 100% |
| 2 | Van Hasselt, H (2013) Estimating the maximum expected value: an analysis of (nested) cross validation and the maximum sample average | 0.405 | 1 | 1 | 100% |
| 3 | Zhang, A., Lipton, Z., Li, M., and Smola, A (2020) Dive into deep learning, chapter 3 exercises | 0.405 | 1 | 1 | 100% |
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