Coresets for near-convex functions

Murad Tukan, Alaa Maalouf, Dan Feldman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Coreset is usually a small weighted subset of n input points in Rd, that provably approximates their loss function for a given set of queries (models, classifiers, etc.). Coresets become increasingly common in machine learning since existing heuristics or inefficient algorithms may be improved by running them possibly many times on the small coreset that can be maintained for streaming distributed data. Coresets can be obtained by sensitivity (importance) sampling, where its size is proportional to the total sum of sensitivities. Unfortunately, computing the sensitivity of each point is problem dependent and may be harder to compute than the original optimization problem at hand. We suggest a generic framework for computing sensitivities (and thus coresets) for wide family of loss functions which we call near-convex functions. This is by suggesting the f-SVD factorization that generalizes the SVD factorization of matrices to functions. Example applications include coresets that are either new or significantly improves previous results, such as SVM, Logistic regression, M-estimators, and ℓz-regression. Experimental results and open source are also provided.

Original languageEnglish
Title of host publicationConference on Neural Information Processing Systems (NeurIPS, formerly NIPS)
Volume2020-December
StatePublished - 2020
Event34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: 6 Dec 202012 Dec 2020

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Conference

Conference34th Conference on Neural Information Processing Systems, NeurIPS 2020
CityVirtual, Online
Period6/12/2012/12/20

Bibliographical note

Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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