Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-reference alignment in high dimensions: sample complexity and
  phase transition   Multi-reference alignment entails estimating a signal in $\mathbb{R}^L$ from
its circularly-shifted and noisy copies. This problem has been studied
thoroughly in recent years, focusing on the finite-dimensional setting (fixed
$L$). Motivated by single-particle cryo-electron microscopy, we analyze the
sample complexity of the problem in the high-dimensional regime $L\to\infty$.
Our analysis uncovers a phase transition phenomenon governed by the parameter
$\alpha = L/(\sigma^2\log L)$, where $\sigma^2$ is the variance of the noise.
When $\alpha>2$, the impact of the unknown circular shifts on the sample
complexity is minor. Namely, the number of measurements required to achieve a
desired accuracy $\varepsilon$ approaches $\sigma^2/\varepsilon$ for small
$\varepsilon$; this is the sample complexity of estimating a signal in additive
white Gaussian noise, which does not involve shifts. In sharp contrast, when
$\alpha\leq 2$, the problem is significantly harder and the sample complexity
grows substantially quicker with $\sigma^2$.

29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci