Section: Overall Objectives
During its last year, the team was reduced. Olivier Catoni and his two PhD students focussed on the study of new statistical models for corpus linguistics and on dimension free bounds for the estimation of the Gram matrix of an i.i.d. sample (possibly in an infinite dimensional Hilbert space) and its application to Principal Component Analysis.
We recall hereafter the themes that were more broadly studied during the lifespan of the project.
We are a research team on machine learning, with an emphasis on statistical methods. Processing huge amounts of complex data has created a need for statistical methods which could remain valid under very weak hypotheses, in very high dimensional spaces. Our aim is to contribute to a robust, adaptive, computationally efficient and desirably non-asymptotic theory of statistics which could be profitable to learning.
Our theoretical studies bear on the following mathematical tools:
We are involved in the following applications:
the improvement of prediction through the on-line aggregation of predictors, with an emphasis on the forecasting of air quality, electricity consumption, production data of oil reservoirs, exchange rates;