## Abstract

Coreset (or core-set) is a small weighted subset Q of an input set P with respect to a given monotonic function f : R → R that provably approximates its fitting loss (Equation presented) to any given x ∈ R^{d}. Using Q we can obtain an approximation of x^{∗} that minimizes this loss, by running existing optimization algorithms on Q. In this work we provide: (i) A lower bound which proves that there are sets with no coresets smaller than n = |P | for general monotonic loss functions. (ii) A proof that, with an additional common regularization term and under a natural assumption that holds e.g. for logistic regression and the sigmoid activation functions, a small coreset exists for any input P. (iii) A generic coreset construction algorithm that computes such a small coreset Q in O(nd + n log n) time, and (iv) Experimental results with open-source code which demonstrate that our coresets are effective and are much smaller in practice than predicted in theory.

Original language | English |
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Pages (from-to) | 21520-21547 |

Number of pages | 28 |

Journal | Proceedings of Machine Learning Research |

Volume | 162 |

State | Published - 2022 |

Event | 39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States Duration: 17 Jul 2022 → 23 Jul 2022 |

### Bibliographical note

Publisher Copyright:Copyright © 2022 by the author(s)

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability