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Real-world large-scale datasets are heteroskedastic and imbalanced -- labelshave varying levels of uncertainty and label distributions are long-tailed.Heteroskedasticity and imbalance challenge deep learning algorithms due to thedifficulty of distinguishing among mislabeled, ambiguous, and rare examples.Addressing heteroskedasticity and imbalance simultaneously is under-explored.We propose a data-dependent regularization technique for heteroskedasticdatasets that regularizes different regions of the input space differently.Inspired by the theoretical derivation of the optimal regularization strengthin a one-dimensional nonparametric classification setting, our approachadaptively regularizes the data points in higher-uncertainty, lower-densityregions more heavily. We test our method on several benchmark tasks, includinga real-world heteroskedastic and imbalanced dataset, WebVision. Our experimentscorroborate our theory and demonstrate a significant improvement over othermethods in noise-robust deep learning.

Heteroskedastic and Imbalanced Deep Learning with Adaptive Regularization