# Monitoring Algorithmic Fairness

arXiv: https://arxiv.org/abs/2305.15979 · HTML: https://mlsanity.com/paper/2305.15979/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 65 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 30 of 31)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [The What-If Tool: Interactive Probing of Machine Learning Models](https://mlsanity.com/paper/1907.04135/) (2019)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [CheXclusion: Fairness gaps in deep chest X-ray classifiers](https://mlsanity.com/paper/2003.00827/) (2020)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [Runaway Feedback Loops in Predictive Policing](https://mlsanity.com/paper/1706.09847/) (2017)
- [Differentially Private Fair Learning](https://mlsanity.com/paper/1812.02696/) (2018)
- [iFair: Learning Individually Fair Data Representations for Algorithmic Decision Making](https://mlsanity.com/paper/1806.01059/) (2018)
- [Verifying Individual Fairness in Machine Learning Models](https://mlsanity.com/paper/2006.11737/) (2020)
- [Average Individual Fairness: Algorithms, Generalization and Experiments](https://mlsanity.com/paper/1905.10607/) (2019)
- [Probabilistic Verification of Fairness Properties via Concentration](https://mlsanity.com/paper/1812.02573/) (2018)
- [Fair Normalizing Flows](https://mlsanity.com/paper/2106.05937/) (2021)
- [PAC Statistical Model Checking for Markov Decision Processes and Stochastic Games](https://mlsanity.com/paper/1905.04403/) (2019)
- [Justicia: A Stochastic SAT Approach to Formally Verify Fairness](https://mlsanity.com/paper/2009.06516/) (2020)
- [Certifying Robustness to Programmable Data Bias in Decision Trees](https://mlsanity.com/paper/2110.04363/) (2021)
- [Fairness-Aware PAC Learning from Corrupted Data](https://mlsanity.com/paper/2102.06004/) (2021)
- [Probabilistic Verification of Neural Networks Against Group Fairness](https://mlsanity.com/paper/2107.08362/) (2021)
- [Runtime Monitoring of Dynamic Fairness Properties](https://mlsanity.com/paper/2305.04699/) (2023)
- [Algorithmic Fairness Verification with Graphical Models](https://mlsanity.com/paper/2109.09447/) (2021)
- [Real-time Stream-based Monitoring](https://mlsanity.com/paper/1711.03829/) (2017)
- [Probabilistic Hyperproperties of Markov Decision Processes](https://mlsanity.com/paper/2005.03362/) (2020)
- [Monitoring Event Frequencies](https://mlsanity.com/paper/1910.06097/) (2019)

## Built on by (most cited first, 8 of 8)

- [Monitoring Algorithmic Fairness under Partial Observations](https://mlsanity.com/paper/2308.00341/) (2023)
- [Stream-Based Monitoring of Algorithmic Fairness](https://mlsanity.com/paper/2501.18331/) (2025)
- [FairSense: Long-Term Fairness Analysis of ML-Enabled Systems](https://mlsanity.com/paper/2501.01665/) (2025)
- [Runtime Monitoring and Enforcement of Conditional Fairness in Generative AIs](https://mlsanity.com/paper/2404.16663/) (2024)
- [Lookahead Counterfactual Fairness](https://mlsanity.com/paper/2412.01065/) (2024)
- [Monitoring of Static Fairness](https://mlsanity.com/paper/2507.03048/) (2025)
- [Algorithmic Fairness: A Runtime Perspective](https://mlsanity.com/paper/2507.20711/) (2025)
- [FairMon: A Tool for Monitoring and Visualizing Algorithmic Fairness](https://mlsanity.com/paper/2609.26123/) (2026)

## Abstract (arXiv)

Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. Our monitors are of two types, and use, respectively, frequentist and Bayesian statistical inference techniques. While the frequentist monitors compute estimates that are objectively correct with respect to the ground truth, the Bayesian monitors compute estimates that are correct subject to a given prior belief about the system's model. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. Although they exhibit different theoretical complexities in certain cases, in our experiments, both frequentist and Bayesian monitors took less than a millisecond to update their verdicts after each observation.