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

April, 2019


We show how any dataset of any modality (time-series, images, sound...) can be approximated by a wellbehaved (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 [1] regarding expressiveness power and generalization of machine learning models.

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