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Demographic Parity Constrained Minimax Optimal Regression under Linear Model

Kazuto Fukuchi · Jun Sakuma

Great Hall & Hall B1+B2 (level 1) #1727
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[ Paper [ Slides [ Poster [ OpenReview
Wed 13 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: We explore the minimax optimal error associated with a demographic parity-constrained regression problem within the context of a linear model. Our proposed model encompasses a broader range of discriminatory bias sources compared to the model presented by Chzhen and Schreuder. Our analysis reveals that the minimax optimal error for the demographic parity-constrained regression problem under our model is characterized by $\Theta(\frac{dM}{n})$, where $n$ denotes the sample size, $d$ represents the dimensionality, and $M$ signifies the number of demographic groups arising from sensitive attributes. Moreover, we demonstrate that the minimax error increases in conjunction with a larger bias present in the model.

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