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.

**Date**: 22 October 2015, 14:15 (Thursday, 2nd week, Michaelmas 2015)**Venue**: 1 South Parks Road

1 South Parks Road OX1 3TGSee location on maps.ox**Details**: Lecture Theatre, Department of Statistics**Speaker**: Prof Gerard Biau (Université Pierre et Marie Curie)**Organiser**: Professor Yee Whye Teh (Department of Statistics, University of Oxford)**Part of**: Statistics, Applied Probability & Operational Research Seminars**Booking required?**: Not required**Audience**: Members of the University only- Editor: Beverley Lane