Online AUC Optimization for Sparse High-Dimensional Datasets
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The Area Under the ROC Curve (AUC) is a widely used performance measure for imbalanced classification arising from many application domains where high-dimensional sparse data is abundant. In such cases, each d dimensional sample has only k non-zero features with k ≪ d, and data arrives sequentially in a streaming form. Current online AUC optimization algorithms have high per-iteration cost 𝒪(d) and usually produce non-sparse solutions in general, and hence are not suitable for handling the data challenge mentioned above. In this paper, we aim to directly optimize the AUC score for high-dimensional sparse datasets under online learning setting and propose a new algorithm, FTRL-AUC. Our proposed algorithm can process data in an online fashion with a much cheaper per-iteration cost 𝒪(k), making it amenable for high-dimensional sparse streaming data analysis. Our new algorithmic design critically depends on a novel reformulation of the U-statistics AUC objective function as the empirical saddle point reformulation, and the innovative introduction of the "lazy update" rule so that the per-iteration complexity is dramatically reduced from 𝒪(d) to 𝒪(k). Furthermore, FTRL-AUC can inherently capture sparsity more effectively by applying a generalized Follow-The-Regularized-Leader (FTRL) framework. Experiments on real-world datasets demonstrate that FTRL-AUC significantly improves both run time and model sparsity while achieving competitive AUC scores compared with the state-of-the-art methods. Comparison with the online learning method for logistic loss demonstrates that FTRL-AUC achieves higher AUC scores especially when datasets are imbalanced.
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