## Abstract

Coreset is usually a small weighted subset of an input set of items, that provably approximates their loss function for a given set of queries (models, classifiers, hypothesis). That is, the maximum (worst-case) error over all queries is bounded. To obtain smaller coresets, we suggest a natural relaxation: coresets whose average error over the given set of queries is bounded. We provide both deterministic and randomized (generic) algorithms for computing such a coreset for any finite set of queries. Unlike most corresponding coresets for the worst-case error, the size of the coreset in this work is independent of both the input size and its Vapnik–Chervonenkis (VC) dimension. The main technique is to reduce the average-case coreset into the vector summarization problem, where the goal is to compute a weighted subset of the n input vectors which approximates their sum. We then suggest the first algorithm for computing this weighted subset in time that is linear in the input size, for n ≫ 1/ε, where ε is the approximation error, improving, e.g., both [ICML’17] and applications for principal component analysis (PCA) [NIPS’16]. Experimental results show significant and consistent improvement also in practice. Open source code is provided.

Original language | English |
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Article number | 6689 |

Journal | Sensors |

Volume | 21 |

Issue number | 19 |

DOIs | |

State | Published - 8 Oct 2021 |

### Bibliographical note

Publisher Copyright:© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

## Keywords

- Approximation algorithms
- Average case analysis
- Big data
- Coreset
- Dimensionality reduction
- Sparsification

## ASJC Scopus subject areas

- Analytical Chemistry
- Information Systems
- Instrumentation
- Atomic and Molecular Physics, and Optics
- Electrical and Electronic Engineering
- Biochemistry