1. Statistical inference of finite-rank tensors
- Author
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Chen, Hong-Bin, Mourrat, Jean-Christophe, Xia, Jiaming, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
FOS: Computer and information sciences ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,82B44, 82D30 ,Information Theory (cs.IT) ,Computer Science - Information Theory ,Probability (math.PR) ,FOS: Mathematics ,FOS: Physical sciences ,Ocean Engineering ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Mathematics - Probability - Abstract
We consider a general statistical inference model of finite-rank tensor products. For any interaction structure and any order of tensor products, we identify the limit free energy of the model in terms of a variational formula. Our approach consists of showing first that the limit free energy must be the viscosity solution to a certain Hamilton-Jacobi equation., 24 pages, final version
- Published
- 2022