Learning probability distributions from smooth observables and the maximum entropy principle: some remarks

8th STATPHYS-KOLKATA

Obuchi, Tomoyuki^1 ; Monasson, Rémi^2

Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Japan^1

Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, Associé Au CNRS et l'Université Pierre et Marie Curie, Paris

75005, France^2

关键词: Engineering tasks;    Inference problem;    Learning probability distributions;    Maximum entropy principle;    Mechanical formulation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/638/1/012018/pdf
DOI  :  10.1088/1742-6596/638/1/012018

来源: IOP

【 摘 要 】

The maximum entropy principle (MEP) is a very useful working hypothesis in a wide variety of inference problems, ranging from biological to engineering tasks. To better understand the reasons of the success of MEP, we propose a statistical-mechanical formulation to treat the space of probability distributions constrained by the measures of (experimental) observables. In this paper we first review the results of a detailed analysis of the simplest case of randomly chosen observables. In addition, we investigate by numerical and analytical means the case of smooth observables, which is of practical relevance. Our preliminary results are presented and discussed with respect to the efficiency of the MEP.