The 2015 AMMCS-CAIMS Congress

Interdisciplinary AMMCS Conference Series

Waterloo, Ontario, Canada | June 7-12, 2015

AMMCS-CAIMS 2015 Plenary Talk

Learning in High Dimension: from Images to Quantum Chemistry

Stéphane Mallat (Ecole Normale Superieure)

Learning from data means approximating functionals in high dimensional spaces. Finding strong sources of regularity is necessary to avoid the curse of dimensionality. Invariance to action of small groups such as rigid displacements is too weak, but stability to action of diffeomorphims is a much stronger property, statisfied by many physical functionals and most signal and image classification problems. We show that it is sufficient to approximate complex high-dimensional classification and regression functionals.

We introduce scattering operators, which are invariants to low-dimensional Lie groups, and Lipschitz continuous to actions of diffeomorphisms. They are computed with iterated multiscale wavelet transforms. These scattering operators provide a Euclidean embedding of geometric distances and a representation of stationary random processes, which captures intermittency phenomena. Applications will be shown for several image classification problems, and for learning quantum chemistry energy functionals.

Stéphane Mallat received the Ph.D. degree in electrical engineering from the University of Pennsylvania, in 1988. He was then Professor at the Courant Institute of Mathematical Sciences. In 1995, he became Professor in Applied Mathematics at Ecole Polytechnique, Paris. From 2001 to 2007 he was co-founder and CEO of a semiconductor start-up company. In 2012 he joined the Computer Science Department of Ecole Normale Supérieure, in Paris.

Stéphane Mallat’s research interests include signal processing, computer vision, harmonic analysis and learning. He wrote a “Wavelet tour of signal processing: the sparse way”. In 1997, he received the Outstanding Achievement Award from the SPIE Society and was a plenary lecturer at the International Congress of Mathematicians in 1998. He also received the 2004 European IST Grand prize, the 2004 INIST-CNRS prize for most cited French researcher in engineering and computer science, and the CNRS innovation medal in 2014. He was elected at the French Academy of Sciences in 2014.