Math Park - 05/13/2017 - DOMINIQUE PICARD, SOME MATHEMATICAL PARADIGMS (...)

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Institut Henri Poincaré

Published on Streamed live on May 13, 2017
About :

Data is now arriving, as we know, in massive quantities. It is the phenomenon of Big Data that poses challenges of all kinds to the modern world, to the point that some proponents of "post-modern rationality" claim to replace human logic with "statistical" logic. Mathematicians clearly have an important card to play in understanding, analyzing and possibly resolving these new challenges. Computer scientists and statisticians are currently at the forefront of these problems, due to their experience in data processing, but many questions in this field require in-depth skills from various parts of mathematics. In this presentation, we will describe several aspects of high-dimensional data processing, focusing on indicating or describing possible or established links with other areas of mathematics. We will talk in particular about "Compressed sensing" or how to reconstruct a signal from only a few linear projections. We will introduce the concepts of l1 decoder and restricted isometry conditions. This will bring us to the notion of concentration in probability and, in particular, that of large random matrices. We will then speak of "sparsity", a Franglais word whose closest French meaning is probably parsimony. We will link this notion to the notion of regularity of functions (Lipschitzian functions for example) and their representation in various bases: trigonometric basis, Haar basis, wavelet basis and, more generally, localized basis associated with the diagonalization of an operator describing a geometry. We will extend these concepts to the fundamental problem of data representation, that is to say, their transformation into a number (ideally small) of functions that allow us to best bring out the salient phenomena. This part will allow us in particular first to use graph Laplacians. ---------------------------------- You can join us on social networks to follow our news. Facebook: / instituthenripoincare Twitter: / inhenripoincare Instagram: / ihp_maisondesmaths

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