An Effective Theory of Bias Amplification
Arjun Subramonian Samuel Bell Levent Sagun Elvis Dohmatob
Machine learning models can capture and amplify biases present in data, leading to disparate test performance across social groups. To better understand, evaluate, and mitigate these biases, a deeper theoretical understanding of how model design choices and data distribution properties contribute to bias is needed. In this work, we contribute a precise analytical theory in the context of ridge regression, both with and without random projections, where the former models feedforward neural networks in a simplified regime. Our theory offers a unified and rigorous explanation of machine learning bias, providing insights into phenomena such as bias amplification and minority-group bias in various feature and parameter regimes. For example, we observe that there may be an optimal regularization penalty or training time to avoid bias amplification, and there can be differences in test error between groups that are not alleviated with increased parameterization. Importantly, our theoretical predictions align with  empirical observations reported in the literature on machine learning bias. We extensively empirically validate our theory on synthetic and semi-synthetic datasets.
fairness, algorithmic bias, machine learning theory, random matrix theory
We present a precise, effective theory of machine learning bias that explains empirical observations found in the literature, such as bias amplification and minority-group bias.