The Statistical Fairness-Accuracy Frontier
summary
Characterizes the fairness-accuracy frontier for two-group linear regression under finite samples: proves minimax-optimal estimators when covariate covariance is known (estimator plugs in sample betas and keeps group covariances) and shows ordinary least squares is minimax when covariances are unknown. Error splits into a bias–variance decomposition where bias (from unknown covariates) scales with ||beta_R−beta_B|| and is symmetric in n_R,n_B while variance scales like 1/√n_R+1/√n_B. Gives optimal sample allocation rules and a uniform confidence band (chaining) bounding sup_lambda error; d=15 simulations match theory.
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chapters (10)
- 0:00Introduction
- 1:27Fairness-accuracy trade-offs
- 4:52Statistical fairness frontier
- 8:12Linear regression setup
- 13:18Approximating frontier with samples
- 19:28Case: Known noise and covariates
- 25:50Case: Known noise variance
- 32:49Uniform bounds for frontier
- 36:12Summary
- 42:42Answering audience questions on extensions
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