Tuesday, 26th of February
14h30 (room R2014, 660 building) (see location
Jean Barbier (ENS Paris & ICTP Trieste)
Title: Phase transitions in high-dimensional estimation and learning
I will present a unified and mathematically rigorous framework allowing to locate the information-theoretic and algorithmic limits in high-dimensional generalized linear models (GLMs). This allows to draw « phase diagrams » as in physics, the phases being associated to different algorithmic behaviors. The GLM includes as special cases plethora of important models in signal processing (compressed-sensing, phase retrieval etc), communications, but also in learning such as the famous perceptron neural network. Many special cases of GLMs have been analyzed in the statistical physics literature, in particular thanks to the heuristic replica method developed in the context of spin glasses. I will discuss recent mathematical tools that vindicate the statistical physics approach, as well as recent findings about the rich algorithmic behaviors encountered in such models.
Contact: guillaume.charpiat at inria.fr
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