Distributed Inference (joint work with K. Bleakley and B. Cadre)
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 3TG
Venue 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