Coresets for Classification – Simplified and StrengthenedDownload PDF

21 May 2021, 20:44 (modified: 26 Oct 2021, 17:31)NeurIPS 2021 PosterReaders: Everyone
Keywords: coresets, logistic regression, importance sampling, leverage score sampling, lewis weight sampling
TL;DR: We use Lewis weight sampling to give improved coresets for logistic and hinge loss regression.
Abstract: 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 by Munteanu et al. 2018. Our result is based on subsampling data points with probabilities proportional to their $\ell_1$ $Lewis$ $weights$. 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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