Biasbound

Biasbound is a term used in statistics and machine learning to denote a formal bound on the bias of an estimator or predictor under a defined class of data-generating processes or modeling assumptions. The bias refers to the difference between the expected value of the estimator and the true quantity being estimated. A biasbound provides a guarantee that this difference does not exceed a specified value, either deterministically or with high probability.

Mathematically, if θ_hat is an estimator of θ, a biasbound states that sup over a class C of data-generating processes E[θ_hat] - θ satisfies |E[θ_hat] - θ| ≤ B, where B may depend on sample size, model complexity, and distributional assumptions.

Derivation methods include concentration inequalities, asymptotic expansions, bias-variance decompositions, regularization-based controls, and bootstrap arguments.

Applications include estimator design, model auditing, and fairness and reliability assessments in predictive systems, especially under distribution shift where unbiasedness cannot be guaranteed.

Limitations include sometimes loose or unverifiable bounds, dependence on modeling assumptions, and the potential for bounds to be vacuous in certain regimes. While biasbounds can aid in comparing estimators and informing risk assessments, they rely on specified conditions and may not always translate into practical performance guarantees across all scenarios.