Statistical and computational phase transitions in spiked tensor estimation
Statistics Theory
2020-01-22 v2 Disordered Systems and Neural Networks
Information Theory
math.IT
Statistics Theory
Abstract
We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Squared 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.
Cite
@article{arxiv.1701.08010,
title = {Statistical and computational phase transitions in spiked tensor estimation},
author = {Thibault Lesieur and Léo Miolane and Marc Lelarge and Florent Krzakala and Lenka Zdeborová},
journal= {arXiv preprint arXiv:1701.08010},
year = {2020}
}
Comments
17 pages, 3 figures, 1 table