Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Universality of Noiseless Linear Estimation with Respect to the
  Measurement Matrix   In a noiseless linear estimation problem, one aims to reconstruct a vector x*
from the knowledge of its linear projections y=Phi x*. There have been many
theoretical works concentrating on the case where the matrix Phi is a random
i.i.d. one, but a number of heuristic evidence suggests that many of these
results are universal and extend well beyond this restricted case. Here we
revisit this problematic through the prism of development of message passing
methods, and consider not only the universality of the l1 transition, as
previously addressed, but also the one of the optimal Bayesian reconstruction.
We observed that the universality extends to the Bayes-optimal minimum
mean-squared (MMSE) error, and to a range of structured matrices.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom