Demographic Parity Constrained Minimax Optimal Regression under Linear Model

TL;DR

This paper analyzes the minimax optimal error in demographic parity-constrained linear regression, revealing how bias and demographic groups influence the error rate, and broadening the understanding of discriminatory bias sources.

Contribution

It introduces a more comprehensive model for demographic parity-constrained regression and characterizes the minimax optimal error as a function of sample size, dimensionality, and bias.

Findings

Minimax error scales as Θ(dM/n).

Error increases with model bias.

Broader bias sources are incorporated compared to prior models.

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 (2022). 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.