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Article Dans Une Revue Journal of Machine Learning Research Année : 2016

The Statistical Performance of Collaborative Inference

Résumé

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 collab-orative 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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Dates et versions

hal-01170254 , version 1 (01-07-2015)
hal-01170254 , version 2 (10-01-2017)

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Gérard Biau, Kevin Bleakley, Benoît Cadre. The Statistical Performance of Collaborative Inference. Journal of Machine Learning Research, 2016, 17. ⟨hal-01170254v2⟩
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