# Matrix Estimation for Individual Fairness

arXiv: https://arxiv.org/abs/2302.02096 · HTML: https://mlsanity.com/paper/2302.02096/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 4 Feb 2023.

## Builds on (most cited first, 19 of 19)

- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [Fairness in Recommendation Ranking through Pairwise Comparisons](https://mlsanity.com/paper/1903.00780/) (2019)
- [Equity of Attention: Amortizing Individual Fairness in Rankings](https://mlsanity.com/paper/1805.01788/) (2018)
- [Beyond Parity: Fairness Objectives for Collaborative Filtering](https://mlsanity.com/paper/1705.08804/) (2017)
- [Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees](https://mlsanity.com/paper/1509.03025/) (2015)
- [On Formalizing Fairness in Prediction with Machine Learning](https://mlsanity.com/paper/1710.03184/) (2017)
- [ME-Net: Towards Effective Adversarial Robustness with Matrix Estimation](https://mlsanity.com/paper/1905.11971/) (2019)
- [Online Learning with an Unknown Fairness Metric](https://mlsanity.com/paper/1802.06936/) (2018)
- [Fairness in Rankings and Recommendations: An Overview](https://mlsanity.com/paper/2104.05994/) (2021)
- [Metric Learning for Individual Fairness](https://mlsanity.com/paper/1906.00250/) (2019)
- [Metric-Free Individual Fairness in Online Learning](https://mlsanity.com/paper/2002.05474/) (2020)
- [Bayesian estimation from few samples: community detection and related problems](https://mlsanity.com/paper/1710.00264/) (2017)
- [Incoherence-Optimal Matrix Completion](https://mlsanity.com/paper/1310.0154/) (2013)
- [Robust Synthetic Control](https://mlsanity.com/paper/1711.06940/) (2017)
- [A Fairness-aware Hybrid Recommender System](https://mlsanity.com/paper/1809.09030/) (2018)
- [Personalizing Fairness-aware Re-ranking](https://mlsanity.com/paper/1809.02921/) (2018)
- [Reducing Crowdsourcing to Graphon Estimation, Statistically](https://mlsanity.com/paper/1703.08085/) (2017)
- [Model Agnostic Time Series Analysis via Matrix Estimation](https://mlsanity.com/paper/1802.09064/) (2018)
- [Neural Fair Collaborative Filtering](https://mlsanity.com/paper/2009.08955/) (2020)

## Built on by (most cited first, 1 of 1)

- [Monotone Individual Fairness](https://mlsanity.com/paper/2403.06812/) (2024)

## Abstract (arXiv)

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.