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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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This content will become publicly available on June 9, 2026
Sampling and Integration of Logconcave Functions by Algorithmic Diffusion
We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions given an evaluation oracle. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and matches the best-known complexities for the special case of uniform distributions on convex bodies. For the sampling problem, our output guarantees are significantly stronger than previously known, and lead to a streamlined analysis of statistical estimation based on dependent random samples.
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- Award ID(s):
- 2106444
- PAR ID:
- 10613755
- Publisher / Repository:
- STOC 2025
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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