License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.30
URN: urn:nbn:de:0030-drops-140994
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14099/
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Blanc, Guy ; Lange, Jane ; Tan, Li-Yang

Learning Stochastic Decision Trees

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LIPIcs-ICALP-2021-30.pdf (0.8 MB)

Abstract

We give a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise. Given an η-corrupted set of uniform random samples labeled by a size-s stochastic decision tree, our algorithm runs in time n^{O(log(s/ε)/ε²)} and returns a hypothesis with error within an additive 2η + ε of the Bayes optimal. An additive 2η is the information-theoretic minimum.
Previously no non-trivial algorithm with a guarantee of O(η) + ε was known, even for weaker noise models. Our algorithm is furthermore proper, returning a hypothesis that is itself a decision tree; previously no such algorithm was known even in the noiseless setting.

BibTeX - Entry

@InProceedings{blanc_et_al:LIPIcs.ICALP.2021.30,
  author =	{Blanc, Guy and Lange, Jane and Tan, Li-Yang},
  title =	{{Learning Stochastic Decision Trees}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14099},
  URN =		{urn:nbn:de:0030-drops-140994},
  doi =		{10.4230/LIPIcs.ICALP.2021.30},
  annote =	{Keywords: Learning theory, decision trees, proper learning algorithms, adversarial noise}
}

Keywords: Learning theory, decision trees, proper learning algorithms, adversarial noise
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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