标题： 协同推理的统计性能 显示英文标题

标题： The Statistical Performance of Collaborative Inference

摘要： 大规模和复杂数据集的统计分析需要依赖分布式计算和协作推理的算法的发展。 受此启发，我们提出了一种协作框架，旨在估计随机变量 $X$ 的未知均值 $\theta$。 在我们提出的模型中，一定数量的计算单元分布在由图表示的通信网络中，通过从 $X$ 接收独立数据并利用定义在图上的随机矩阵 $A$ 进行消息交换，参与对 $\theta$ 的估计。 我们给出了关于矩阵 $A$ 的精确条件，使得各个单元的统计精度可以与（黄金标准）虚拟集中式估计相当，尽管每个单元无法访问所有数据。 我们特别展示了 $A$ 的非平凡特征值以及拉马努金类扩展图所起的根本作用，它们在适度的算法成本下提供了卓越的性能。 显示英文摘要

摘要： The statistical analysis of massive and complex data sets will require the development of algorithms that depend on distributed computing and collaborative inference. Inspired by this, we propose a collaborative framework that aims to estimate the unknown mean $\theta$ of a random variable $X$. In the model we present, a certain number of calculation units, distributed across a communication network represented by a graph, participate in the estimation of $\theta$ by sequentially receiving independent data from $X$ while exchanging messages via a stochastic matrix $A$ defined over the graph. We give precise conditions on the matrix $A$ under which the statistical precision of the individual units is comparable to that of a (gold standard) virtual centralized estimate, even though each unit does not have access to all of the data. We show in particular the fundamental role played by both the non-trivial eigenvalues of $A$ and the Ramanujan class of expander graphs, which provide remarkable performance for moderate algorithmic cost.