Real numbers, data science and chaos: How to fit any dataset with a single parameter

Laurent Boué
4/28/2019
cs.LGcs.DMcs.IR

Official code: Ranlot/single-parameter-fit (650 stars, last commit 2022-11-22).

Abstract

We show how any dataset of any modality (time-series, images, sound...) can be approximated by a well-behaved (continuous, differentiable...) scalar function with a single real-valued parameter. Building upon elementary concepts from chaos theory, we adopt a pedagogical approach demonstrating how to adjust this parameter in order to achieve arbitrary precision fit to all samples of the data. Targeting an audience of data scientists with a taste for the curious and unusual, the results presented here expand on previous similar observations regarding expressiveness power and generalization of machine learning models.

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Code Implementations(1)

Ranlot/single-parameter-fitOfficial100%

Real numbers, data science and chaos: How to fit any dataset with a single parameter

65057TeX, ShellApr 27, 20193 years ago
chaos-theorygoodness-of-fitmachine-learning

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Cite this paper

@article{bou2019real,
  title  = {Real numbers, data science and chaos: How to fit any dataset with a single parameter},
  author = {Laurent Boué},
  year   = {2019},
  eprint = {1904.12320},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1904.12320}
}

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