Generic Coreset for Scalable Learning of Monotonic Kernels: Logistic Regression, Sigmoid and more

Elad Tolochinsky, Ibrahim Jubran, Dan Feldman

Research output: Contribution to journalConference articlepeer-review


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 ∈ Rd. 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 languageEnglish
Pages (from-to)21520-21547
Number of pages28
JournalProceedings of Machine Learning Research
StatePublished - 2022
Event39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States
Duration: 17 Jul 202223 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


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