Team : mistis
Section: Scientific Foundations
Keywords : non parametric, boundary estimation, extremes, wavelets, scaling laws, singularity spectra.
Functional Inference, semi and non parametric methods
We also consider methods which do not assume a parametric model. Such methods are used for instance to study distribution tails without introducing a parametric model on the data: this is part of the extreme values theory. Similarly, the grey-levels surface in an image cannot usually be described through a simple mathematical equation. Projection methods are then a way to decompose the unknown signal or image on a set of functions (e.g. wavelets). Kernel methods which rely on smoothing the data using a set of kernels (usually probability distributions), are other examples. Relationships exist between these methods and learning techniques using Support Vector Machine (SVM) as this appears in the context of boundary estimation. As regards wavelets, our goal is to propose wavelet based estimators aimed at characterizing and analyzing scaling laws structures of processes or systems. The compression/dilation operator, at the core of wavelet analysis, allows to identify complex scale organizations, such as 1/f type processes (e.g.mono-fractals), high order statistics governed by power laws (e.g. multi-fractals), or more generally cascade type constructions of measures and processes.