  Ensuring fair predictions across many distinct subpopulations in the training
data can be prohibitive for large models. Recently, simple linear last layer
retraining strategies, in combination with data augmentation methods such as
upweighting, downsampling and mixup, have been shown to achieve
state-of-the-art performance for worst-group accuracy, which quantifies
accuracy for the least prevalent subpopulation. For linear last layer
retraining and the abovementioned augmentations, we present the optimal
worst-group accuracy when modeling the distribution of the latent
representations (input to the last layer) as Gaussian for each subpopulation.
We evaluate and verify our results for both synthetic and large publicly
available datasets.
