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We give relative error coresets for training linear classifiers with a broad class of loss functions, including the logistic loss and hinge loss. Our construction achieves $$(1\pm \epsilon)$$ relative error with $$\tilde O(d \cdot \mu_y(X)^2/\epsilon^2)$$ points, where $$\mu_y(X)$$ is a natural complexity measure of the data matrix $$X \in \mathbb{R}^{n \times d}$$ and label vector $$y \in \{-1,1\}^n$$, introduced in Munteanu et al. 2018. Our result is based on subsampling data points with probabilities proportional to their \textit{$$\ell_1$$ Lewis weights}. It significantly improves on existing theoretical bounds and performs well in practice, outperforming uniform subsampling along with other importance sampling methods. Our sampling distribution does not depend on the labels, so can be used for active learning. It also does not depend on the specific loss function, so a single coreset can be used in multiple training scenarios.
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No Dimensional Sampling Coresets for Classification
We refine and generalize what is known about coresets for classification problems via the sensitivity sampling framework. Such coresets seek the smallest possible subsets of input data, so one can optimize a loss function on the coreset and ensure approximation guarantees with respect to the original data. Our analysis provides the first no dimensional coresets, so the size does not depend on the dimension. Moreover, our results are general, apply for distributional input and can use iid samples, so provide sample complexity bounds, and work for a variety of loss functions. A key tool we develop is a Radamacher complexity version of the main sensitivity sampling approach, which can be of independent interest.
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- Award ID(s):
- 2115677
- PAR ID:
- 10537703
- Publisher / Repository:
- Proceedings of the 41st International Conference on Machine Learning (ICML)
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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