Processing data to validate a hypothesis or estimate parameters has long been the exclusive domain of statistics. However, as the dimensions of data have increased, the Combinatorics of possibilities has exploded. This curse of dimensionality is a central difficulty in data analysis, be it images, sounds, texts, or experimental measurements as in physics, biology or economics. Modeling and representing the hidden structures of data calls on various branches of mathematics, but also on computer science. Statistical learning algorithms, such as neural networks, are configured to optimize the analysis of data based on examples. They are behind the spectacular results of artificial intelligence. Their scientific, industrial and societal applications are considerable, and their performance is progressing much faster than our mastery of their mathematical properties.

The Chair offers lectures in applied mathematics, bridging the gap between the jungle of new algorithmic developments and an understanding of the underlying general principles. Applications cover all aspects of signal processing and statistical learning. In addition to statistics and probability, harmonic analysis, optimization and geometry are also covered. The study of applications and new algorithms is proposed within the framework of data challenges, which are organized by the Chair.

Stéphane Mallat's research team at ENS is studying principles for structuring data analysis to escape the curse of dimensionality. In particular, it is developing neural network models based on the principles of wavelet scale separation, parsimony and invariance. Applications range from image and sound recognition to the estimation of physical measurements. For further information, please visit the research team'swebsite.