Coresets for Decision Trees of Signals

Ibrahim Jubran, Ernesto Evgeniy Sanches Shayda, Ilan Newman, Dan Feldman

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


A k-decision tree t (or k-tree) is a recursive partition of a matrix (2D-signal) into k ≥ 1 block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to a given matrix D of N entries (labels) is the sum of squared differences over every label in D and its assigned label by t. Given an error parameter ε ∈ (0, 1), a (k, ε)-coreset C of D is a small summarization that provably approximates this loss to every such tree, up to a multiplicative factor of 1 ± ε. In particular, the optimal k-tree of C is a (1 + ε)-approximation to the optimal k-tree of D. We provide the first algorithm that outputs such a (k, ε)-coreset for every such matrix D. The size |C| of the coreset is polynomial in k log(N)/ε, and its construction takes O(Nk) time. This is by forging a link between decision trees from machine learning – to partition trees in computational geometry. Experimental results on sklearn and lightGBM show that applying our coresets on real-world data-sets boosts the computation time of random forests and their parameter tuning by up to x10, while keeping similar accuracy. Full open source code is provided.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
EditorsMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
PublisherNeural information processing systems foundation
Number of pages13
ISBN (Electronic)9781713845393
StatePublished - 7 Oct 2021
Event35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Duration: 6 Dec 202114 Dec 2021

Publication series

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


Conference35th Conference on Neural Information Processing Systems, NeurIPS 2021
CityVirtual, Online

Bibliographical note

Funding Information:
This research was supported by The ISRAEL SCIENCE FOUNDATION, grant number 379/21.

Publisher Copyright:
© 2021 Neural information processing systems foundation. All rights reserved.


  • cs.LG
  • cs.DS

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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