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Fast and fully-automated histograms for large-scale data sets

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  • Zelaya Mendizábal, Valentina
  • Boullé, Marc
  • Rossi, Fabrice

Abstract

G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the Minimum Description Length principle (MDL) to derive two different model selection criteria. Several proven theoretical results about these criteria give insights about their asymptotic behaviour and are used to speed up their optimisation. These insights, combined to a greedy search heuristic, are used to construct histograms in linearithmic time rather than the polynomial time incurred by previous works. The capabilities of the proposed MDL density estimation method are illustrated with reference to other fully automated methods in the literature, both on synthetic and large real-world data sets.

Suggested Citation

  • Zelaya Mendizábal, Valentina & Boullé, Marc & Rossi, Fabrice, 2023. "Fast and fully-automated histograms for large-scale data sets," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002481
    DOI: 10.1016/j.csda.2022.107668
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    References listed on IDEAS

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    1. Peter D. Grünwald, 2007. "The Minimum Description Length Principle," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262072815, December.
    2. Rozenholc, Yves & Mildenberger, Thoralf & Gather, Ursula, 2010. "Combining regular and irregular histograms by penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3313-3323, December.
    3. Charles R. Harris & K. Jarrod Millman & Stéfan J. Walt & Ralf Gommers & Pauli Virtanen & David Cournapeau & Eric Wieser & Julian Taylor & Sebastian Berg & Nathaniel J. Smith & Robert Kern & Matti Picu, 2020. "Array programming with NumPy," Nature, Nature, vol. 585(7825), pages 357-362, September.
    4. Housen Li & Axel Munk & Hannes Sieling & Guenther Walther, 2020. "The essential histogram," Biometrika, Biometrika Trust, vol. 107(2), pages 347-364.
    5. Celisse, Alain & Robin, Stephane, 2008. "Nonparametric density estimation by exact leave-p-out cross-validation," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2350-2368, January.
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