Section: New Results

Statistical learning methodology and theory

Participants : Gilles Celeux, Christine Keribin, Erwan Le Pennec, Michel Prenat, Solenne Thivin, Kevin Bleakley.

Gilles Celeux has started a collaboration with Jean-Patrick Baudry on strategies to avoid traps in the EM algorithm in mixture analysis. They analyze the effect of spurious local maximizers, and regularized algorithms to avoid such solutions. They show the link that exists between the degree of regularization and slope heuristics. Moreover, their strategy to initiate the EM algorithm, embedding the solution with $K$ components and the starting position with $K+1$ components to avoid suboptimal solutions, has been proved to be efficient, and is extended to a more complex framework of latent block models.

In the context of algorithms that depend on distributed computing and collaborative inference, Kevin Bleakley, with with Gérard Biau (LSTA, Paris 6) and Benoït Cadre (ENS Rennes), have proposed a collaborative framework that aims to estimate the unknown mean $\theta$ of a random variable $X$. In the model they 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. They 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.