# Fairness in Forecasting of Observations of Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2209.05274 · HTML: https://mlsanity.com/paper/2209.05274/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 119 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 30 of 54)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [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)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [On the Privacy Risks of Algorithmic Fairness](https://mlsanity.com/paper/2011.03731/) (2020)
- [Robust Optimization for Fairness with Noisy Protected Groups](https://mlsanity.com/paper/2002.09343/) (2020)
- [Learning Optimal and Fair Decision Trees for Non-Discriminative Decision-Making](https://mlsanity.com/paper/1903.10598/) (2019)
- [Finite Sample Analysis of Stochastic System Identification](https://mlsanity.com/paper/1903.09122/) (2019)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [On Formalizing Fairness in Prediction with Machine Learning](https://mlsanity.com/paper/1710.03184/) (2017)
- [Post-processing for Individual Fairness](https://mlsanity.com/paper/2110.13796/) (2021)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Algorithms for Fairness in Sequential Decision Making](https://mlsanity.com/paper/1901.08568/) (2019)
- [Discrimination in the Age of Algorithms](https://mlsanity.com/paper/1902.03731/) (2019)
- [Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?](https://mlsanity.com/paper/1912.01094/) (2019)
- [On the relation between accuracy and fairness in binary classification](https://mlsanity.com/paper/1505.05723/) (2015)
- [Learning Linear Dynamical Systems via Spectral Filtering](https://mlsanity.com/paper/1711.00946/) (2017)
- [Average Individual Fairness: Algorithms, Generalization and Experiments](https://mlsanity.com/paper/1905.10607/) (2019)
- [Empirical observation of negligible fairness-accuracy trade-offs in machine learning for public policy](https://mlsanity.com/paper/2012.02972/) (2020)
- [Causal Conceptions of Fairness and their Consequences](https://mlsanity.com/paper/2207.05302/) (2022)

## Built on by (most cited first, 4 of 4)

- [Fairness in Ranking: Robustness through Randomization without the Protected Attribute](https://mlsanity.com/paper/2403.19419/) (2024)
- [Improving the Validity of Decision Trees as Explanations](https://mlsanity.com/paper/2306.06777/) (2023)
- [Benchmarking Stochastic Approximation Algorithms for Fairness-Constrained Training of Deep Neural Networks](https://mlsanity.com/paper/2507.04033/) (2025)
- [humancompatible.detect: a Python Toolkit for Detecting Bias in AI Models](https://mlsanity.com/paper/2509.24340/) (2025)

## Abstract (arXiv)

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. This behaviour can often be modelled as observations of an unknown dynamical system with an unobserved state. When the training data for the subgroups are not controlled carefully, however, under-representation bias arises. To counter under-representation bias, we introduce two natural notions of fairness in time-series forecasting problems: subgroup fairness and instantaneous fairness. These notions extend predictive parity to the learning of dynamical systems. We also show globally convergent methods for the fairness-constrained learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. We also show that by exploiting sparsity in the convexifications, we can reduce the run time of our methods considerably. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate the efficacy of our methods.