When Can Memorization Improve Fairness?
Bob Pepin, Christian Igel, Raghavendra Selvan
TL;DR
The paper analyzes when memorizing a subpopulation can improve additive fairness metrics ($\Delta_{s.p.}$, $\Delta_{eq.opp.}$, $\Delta_{eq.odds}$) in multi-class classification by modeling memorization as perfect predictions on a subset with data mass $p_D$. It derives explicit bias expressions for each metric in terms of population and memorized-subpopulation distributions ($p^+$, $q_y$, $q_y^+$, etc.) and base-classifier statistics, and shows that these biases scale with $p_D$ and depend on class-group imbalances. It characterizes zero-bias memorized configurations via linear-constraint systems, providing necessary and sufficient conditions and upper/lower bounds on the memorized mass needed to eliminate bias for SP and Equal Opportunity, with a rare, ratio-based condition for Equalized Odds. The results offer a principled framework for understanding and preventing bias amplification due to memorization, informing dataset design and defenses against metric gaming in fair ML workflows.
Abstract
We study to which extent additive fairness metrics (statistical parity, equal opportunity and equalized odds) can be influenced in a multi-class classification problem by memorizing a subset of the population. We give explicit expressions for the bias resulting from memorization in terms of the label and group membership distribution of the memorized dataset and the classifier bias on the unmemorized dataset. We also characterize the memorized datasets that eliminate the bias for all three metrics considered. Finally we provide upper and lower bounds on the total probability mass in the memorized dataset that is necessary for the complete elimination of these biases.