Section: New Results

Curves classification, denoising and forecasting

Participants : Émilie Devijver, Pascal Massart, Jean-Michel Poggi, Vincent Thouvenot.

In collaboration with Farouk Mhamdi and Meriem Jaidane (ENIT, Tunis, Tunisia), Jean-Michel Poggi proposed a method for trend extraction from seasonal time series through the Empirical Mode Decomposition (EMD). Experimental comparison of trend extraction based on EMD, X11, X12 and Hodrick Prescott filter are conducted. First results show the eligibility of the blind EMD trend extraction method. Tunisian real peak load is also used to illustrate the extraction of the intrinsic trend.

Jean-Michel Poggi, co-supervising with Anestis Antoniadis (Université Joseph Fourier Grenoble) the PhD thesis of Vincent Thouvenot, funded by a CIFRE with EDF. The industrial motivation of this work is the recent development of new technologies for measuring power consumption by EDF to acquire consumption data for different mesh network. The thesis will focus on the development of new statistical methods for predicting power consumption by exploiting the different levels of aggregation of network data collection. From the mathematical point of view, the work is to develop generalized additive models for this type of kind of aggregated data for the modeling of functional data, associating closely nonparametric estimation and variable selection using various penalization methods.

Jean-Michel Poggi and Pascal Massart are the co-advisors of the PhD thesis of Émilie Devijver, strongly motivated by the same kind of industrial forecasting problems in electricity, which is dedicated to curves clustering for the prediction. A natural framework to explore this question is mixture of regression models for functional data. They extend to functional data the recent work by Bühlmann and coauthors dealing with the simultaneous estimation of mixture regression models in the scalar case using Lasso type methods. It is based on the technical tools of the work of Caroline Meynet (which completes her thesis Orsay under the direction of P. Massart), which deals with the clustering of functional data using Lasso methods choosing simultaneously number of clusters and selecting significant wavelet coefficients. Nevertheless, they also propose a procedure dealing with low rank estimator. Simulations and benchmark data have been conducted for high-dimensional finite mixture regression models.

Jean-Michel Poggi, co-supervising with Meriem Jaëdane, Raja Ghozi (ENIT Tunisie) and from the industrial side, Sylvie Sevestre-Ghalila (CEA LinkLab), the PhD thesis of Neska El Haouij, funded by a kind of CIFRE with CEA LinkLab. The industrial motivation of this work is the recent development of new technologies for sensory measurements, environmental and physiological to explain and improve the driving tasks . The thesis aims to explain sensory aspects involved in automated decision to the car interior, by objectivization. The thesis will focus on the use and development of experimental designs and statistical methods to quantify and explain driving ability in to the modeling using functional explanatory factors. Statistical contributions of this work will involve nonparametric estimation and variable selection and/or models.