Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Gaussian Mean Estimation under Communication Constraints:
  Optimal Rates and Communication-Efficient Algorithms   We study distributed estimation of a Gaussian mean under communication
constraints in a decision theoretical framework. Minimax rates of convergence,
which characterize the tradeoff between the communication costs and statistical
accuracy, are established in both the univariate and multivariate settings.
Communication-efficient and statistically optimal procedures are developed. In
the univariate case, the optimal rate depends only on the total communication
budget, so long as each local machine has at least one bit. However, in the
multivariate case, the minimax rate depends on the specific allocations of the
communication budgets among the local machines.
  Although optimal estimation of a Gaussian mean is relatively simple in the
conventional setting, it is quite involved under the communication constraints,
both in terms of the optimal procedure design and lower bound argument. The
techniques developed in this paper can be of independent interest. An essential
step is the decomposition of the minimax estimation problem into two stages,
localization and refinement. This critical decomposition provides a framework
for both the lower bound analysis and optimal procedure design.

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The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th