Matrix Estimation for Individual Fairness

TL;DR

This paper demonstrates that matrix estimation, specifically singular value thresholding, can be used as a pre-processing step to improve individual fairness in algorithms without compromising their predictive performance, supported by theoretical guarantees and empirical validation.

Contribution

It establishes a novel connection between matrix estimation and individual fairness, showing that ME pre-processing enhances fairness guarantees without affecting accuracy.

Findings

ME pre-processing improves individual fairness guarantees.

SVT provides near-minimax optimal estimates under certain conditions.

No fairness-performance trade-off observed in experiments.

Abstract

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.