Statistical inference of finite-rank tensors

Hong-Bin Chen; Jean-Christophe Mourrat; Jiaming Xia

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arXiv · 2104.05360

Statistical inference of finite-rank tensors

Hong-Bin Chen·Jean-Christophe Mourrat·Jiaming Xia

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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.

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math.PR cond-mat.dis-nn cs.IT math.IT

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BibTeX RIS

Hong-Bin Chen, Jean-Christophe Mourrat, Jiaming Xia. 2021-04-12. Statistical inference of finite-rank tensors. https://arxiv.org/abs/2104.05360

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