Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical and computational phase transitions in spiked tensor
  estimation   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.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin