Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strong converse bound for multiple hypothesis testing, with
  applications to high-dimensional estimation   In statistical inference problems, we wish to obtain lower bounds on the
minimax risk, that is to bound the performance of any possible estimator. A
standard technique to obtain risk lower bounds involves the use of Fano's
inequality. In an information-theoretic setting, it is known that Fano's
inequality typically does not give a sharp converse result (error lower bound)
for channel coding problems. Moreover, recent work has shown that an argument
based on binary hypothesis testing gives tighter results. We adapt this
technique to the statistical setting, and argue that Fano's inequality can
always be replaced by this approach to obtain tighter lower bounds that can be
easily computed and are asymptotically sharp. We illustrate our technique in
three applications: density estimation, active learning of a binary classifier,
and compressed sensing, obtaining tighter risk lower bounds in each case.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th