Work

Statistical and computational phase transitions in spiked tensor estimation

Year: 2017

Type: conference-paper

Abstract: We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Square Error (MMSE), and unveil information-theoretic phase transitions. In addition, we study the performance of Approximate Message Passing (AMP) and show that it achieves the MMSE for a large set of parameters, and that factorization is algorithmically “easy” in a much wider region than previously believed. It exists, however, a “hard” region where AMP fails to reach the MMSE and we conjecture that no polynomial algorithm will improve on AMP.

Source: IEEE International Symposium on Information Theory (ISIT)

DOI: 10.1109/isit.2017.8006580

Authors: Thibault Lesieur, Leo Miolane, Marc Lelarge, Florent Krzakala, Lenka Zdeborova

Institutions: Université Paris-Saclay, Institut de Physique Théorique, Institut national de recherche en sciences et technologies du numérique, École Normale Supérieure - PSL, Université Paris Sciences et Lettres, Sorbonne Université

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2585411378

FWCI: 6.835

Cites: 24

Cited by: 90

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