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Grouping strategies for denoising

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We investigate the statistical learning approach for modeling various applications. This modeling involves several phases which need to be solved : the first one often is an approximation step, where we need to translate the observations into a dictionary. The choice of this dictionary (wavelets, needlets, variouslets,..., combinations of several bases,...) often conceals a significant part of investigation. The second phase is the treatment of very high dimensional data (ultra-high dimension means that the number of parameters may grow exponentially faster than the number of observations). This phase is requiring optimization methods of different style : $l_1$ minimizers, multi steps methods,..., as well as concentration inequalities. We concentrate on two steps thresholding methods and observe that making groups in the coefficients can seriously improve the selection and prediction rates. We provide a ‘boosting-grouping’ strategy, taking into account this observation.

This talk is part of the Statistics series.

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