Berlin 2024 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 34: Poster: Machine Learning, Data Science, and Reservoir Computing

DY 34.9: Poster

Mittwoch, 20. März 2024, 15:00–18:00, Poster C

Cumulative entropy as a bridge between statistical physics and statistical machine learning — •Hans Reimann and Karoline Wiesner — University of Potsdam, Germany

Cumulative entropies, such as cumulative Shannon entropies or Phi-entropies, have been of growing interest to tackle shortcomings of classical notions of entropy while keeping as many of the desired properties as possible. Some context driven intuitions and overarching frameworks managed to provide some independent insights, yet they are not fully understood or incorporated in well established physical or statistical contexts is still work in progress. We investigate towards statistical and physical properties as well as understanding of the cumulative paired Shannon entropy (CPE) as a promising special case. Utilizing tools from mathematical statistics in combination with information theory our work paves the way toward a thorough understanding along the lines of well established notions of entropy. Next to some first results on parametric and non-parametric estamation and asymptotic properties, we managed to relate the CPE in its most striking properties to both concpets of equilibrium statistics and thermodynamics as well as statistical data analysis. Moreover, we work on expanding these ideas to recent results in physics informed machine learning for binary classification tasks via arguing for the CPE to be a measure of a natural degree of seperability under considerations of Jaynes' understanding of maximum Shannon entropy.

Keywords: Cumulative entropy; Fermi-Dirac statistics; binary classification; binary Shannon entropy; measure of deviation