Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rate-optimal posterior contraction for sparse PCA   Principal component analysis (PCA) is possibly one of the most widely used
statistical tools to recover a low-rank structure of the data. In the
high-dimensional settings, the leading eigenvector of the sample covariance can
be nearly orthogonal to the true eigenvector. A sparse structure is then
commonly assumed along with a low rank structure. Recently, minimax estimation
rates of sparse PCA were established under various interesting settings. On the
other side, Bayesian methods are becoming more and more popular in
high-dimensional estimation, but there is little work to connect frequentist
properties and Bayesian methodologies for high-dimensional data analysis. In
this paper, we propose a prior for the sparse PCA problem and analyze its
theoretical properties. The prior adapts to both sparsity and rank. The
posterior distribution is shown to contract to the truth at optimal minimax
rates. In addition, a computationally efficient strategy for the rank-one case
is discussed.

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc