Maximum Weighted Loss Discrepancy
This addresses fairness and robustness issues in machine learning by providing a new metric for group loss disparities, though it is incremental in building on existing fairness concepts.
The paper introduces maximum weighted loss discrepancy (MWLD) to measure inequality in losses across groups, showing that loss variance regularization can halve loss variance and reduce MWLD without significant accuracy drops.
Though machine learning algorithms excel at minimizing the average loss over a population, this might lead to large discrepancies between the losses across groups within the population. To capture this inequality, we introduce and study a notion we call maximum weighted loss discrepancy (MWLD), the maximum (weighted) difference between the loss of a group and the loss of the population. We relate MWLD to group fairness notions and robustness to demographic shifts. We then show MWLD satisfies the following three properties: 1) It is statistically impossible to estimate MWLD when all groups have equal weights. 2) For a particular family of weighting functions, we can estimate MWLD efficiently. 3) MWLD is related to loss variance, a quantity that arises in generalization bounds. We estimate MWLD with different weighting functions on four common datasets from the fairness literature. We finally show that loss variance regularization can halve the loss variance of a classifier and hence reduce MWLD without suffering a significant drop in accuracy.