How does overparametrization affect performance on minority groups?

Saptarshi Roy, Subha Maity, Songkai Xue, Mikhail Yurochkin, Yuekai Sun

Abstract: The benefits of overparameterization for the overall performance of modern machine learning (ML) models are well known. However, the effect of overparameterization at a more granular level of data subgroups is less understood. Recent empirical studies demonstrate encouraging results: (i) when groups are not known, overparameterized models trained with empirical risk minimization (ERM) perform better on minority groups; (ii) when groups are known, ERM on data subsampled to equalize group sizes yields state-of-the-art worst-group accuracy in the overparameterized regime. In this paper, we complement these empirical studies with a theoretical investigation of the risk of overparameterized random feature regression models on minority groups with identical feature distribution as the majority group. In a setting in which the regression functions for the majority and minority groups are different, we show that overparameterization either improves or does not harm the asymptotic minority group performance under the ERM setting when the features are distributed uniformly over the sphere.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

We apologize for the late response, and we thank the AE and all the referees for their constructive comments that helped improve the paper. We have revised our draft with the following minor revisions as requested by the AE and the referees:

- We have added a new experiment in Appendix D featuring the California Housing dataset. Here, the target is to predict the median house price, and we find that overparameterization in a random feature regression model improves mean squared error for the minority group comprising inland houses. We point this out in the Introduction section (Page 2, Paragraph 2).

- We have provided a simulation study for the classification setting in Appendix E. We find that overparametrization indeed improved the misclassification error for the minority group when the difference between the majority and minority groups is relatively small. This matches the findings in [1]. However, under larger disparity between the majority and minority groups, we find that overparameterization aggravates the misclassification error, similar to the findings in [2]. We also mention this in the paragraph before Section 1.1 (Page 4).

- We have also added new references in the discussion in Section 1.1. The current references include some contemporary works that aim to induce fairness under the DRO, performative prediction, and active learning settings.

[1] Pham, A., Chan, E., Srivatsa, V., Ghosh, D., Yang, Y., Yu, Y., ... & Steinhardt, J. (2021). The effect of model size on worst-group generalization. arXiv preprint arXiv:2112.04094.

[2] Sagawa, S., Raghunathan, A., Koh, P. W., & Liang, P. (2020, November). An investigation of why overparameterization exacerbates spurious correlations. In International Conference on Machine Learning (pp. 8346-8356). PMLR.

Code: https://github.com/smaityumich/overparameterized-group-fairness

Assigned Action Editor: ~Ahmad_Beirami1

Submission Number: 4555