Section: New Results

Statistical learning methodology and theory

Participants : Vincent Brault, Gilles Celeux, Christine Keribin, Erwan Le Pennec, Lucie Montuelle, Mesrob Ohannessian, Michel Prenat, Solenne Thivin.

Gilles Celeux, Christine Keribin and the Ph D. student Vincent Brault continued their study on the Latent Block Model (LBM), and worked more especially on categorical data. They further investigated a Gibbs algorithm to avoid solutions with empty clusters on synthetic as well as real data (Congressional Voting Records and genomic data) [STCO13].They detailed the link between the information criteria ICL and BIC, compared them on synthetic and real data, and conjectured that these criteria are both consistent for LBM, which is not a standard behavior. ICL has been proved to be preferred for LBM.

V. Brault applied the Large Gaps algorithm and compared it with other existing algorithms [Aussois13]. He also derived a CEM algorithm for categorical LBM [Agroselect13]. In partnership with the Inria- MODAL team, he implemented the algorithms and information criteria in the R package blockcluster.

C. Keribin has started a collaboration with Tristan Mary-Huard (AgroParisTech) by the supervision of an internship (Master 2) on the use of LBM with truncated Poisson data.

Erwan Le Pennec is supervising Solenne Thivin in her CIFRE with Michel Prenat and Thales Optronique. The aim is target detection on complex background such as clouds or sea. Their approach is a local approach based on test decision theory. They have obtained theoretical and numerical results on a segmentation based approach in which a simple Markov field testing procedure is used in each cell of a data driven partition.

Erwan Le Pennec and Michel Prenat have also collaborated on a cloud texture modeling using a non-parametric approach. Such a modeling coud be used to better calibrate the detection procedure: it can lead to more examples than the one acquired and it could be the basis of an ensemble method.

Mesrob Ohannessian joined select through an ERCIM Alain Bensoussan fellowship. During his stay, his work focused on two different aspects of statistics: large datasets and data scarcity. In collaboration with researchers in ETH Zurich (Prof. Andreas Krause), he studied the possibility of trading off statistical performance and computational speed in the context of $k$-means clustering, using the notion of coresets. In collaboration with researchers in Paris 11 (Prof. Elisabeth Gassiat) and Paris 7 (Prof. Stéphane Boucheron), he worked on adaptive universal compression when the alphabet is very large, meaning that some symbol observations are scarce.