Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal convex lifted sparse phase retrieval and PCA with an atomic
  matrix norm regularizer   We present novel analysis and algorithms for solving sparse phase retrieval
and sparse principal component analysis (PCA) with convex lifted matrix
formulations. The key innovation is a new mixed atomic matrix norm that, when
used as regularization, promotes low-rank matrices with sparse factors. We show
that convex programs with this atomic norm as a regularizer provide
near-optimal sample complexity and error rate guarantees for sparse phase
retrieval and sparse PCA. While we do not know how to solve the convex programs
exactly with an efficient algorithm, for the phase retrieval case we carefully
analyze the program and its dual and thereby derive a practical heuristic
algorithm. We show empirically that this practical algorithm performs similarly
to existing state-of-the-art algorithms.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc