Learning Small Decision Trees With Few Outliers: A Parameterized Perspective

Harmender Gahlawat, Meirav Zehavi

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

Abstract

Decision trees are a fundamental tool in machine learning for representing, classifying, and generalizing data. It is desirable to construct “small” decision trees, by minimizing either the size (s) or the depth (d) of the decision tree (DT). Recently, the parameterized complexity of DECISION TREE LEARNING has attracted a lot of attention. We consider a generalization of DECISION TREE LEARNING where given a classification instance E and an integer t, the task is to find a “small” DT that disagrees with E in at most t examples. We consider two problems: DTSO and DTDO, where the goal is to construct a DT minimizing s and d, respectively. We first establish that both DTSO and DTDO are W[1]-hard when parameterized by s+δmax and d+δmax, respectively, where δmax is the maximum number of features in which two differently labeled examples can differ. We complement this result by showing that these problems become FPT if we include the parameter t. We also consider the kernelization complexity of these problems and establish several positive and negative results for both DTSO and DTDO.

Original languageEnglish
Title of host publicationTechnical Tracks 14
EditorsMichael Wooldridge, Jennifer Dy, Sriraam Natarajan
PublisherAssociation for the Advancement of Artificial Intelligence
Pages12100-12108
Number of pages9
Edition11
ISBN (Electronic)1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 1577358872, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879, 9781577358879
DOIs
StatePublished - 25 Mar 2024
Event38th AAAI Conference on Artificial Intelligence, AAAI 2024 - Vancouver, Canada
Duration: 20 Feb 202427 Feb 2024

Publication series

NameProceedings of the AAAI Conference on Artificial Intelligence
Number11
Volume38
ISSN (Print)2159-5399
ISSN (Electronic)2374-3468

Conference

Conference38th AAAI Conference on Artificial Intelligence, AAAI 2024
Country/TerritoryCanada
CityVancouver
Period20/02/2427/02/24

ASJC Scopus subject areas

  • Artificial Intelligence

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