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The Statistical Performance of Collaborative Inference

Gérard Biau, Kevin Bleakley, Benoît Cadre.

Year: 2016, Volume: 17, Issue: 62, Pages: 1−29


Abstract

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 θ 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 θ 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.

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