Abstract:
I will introduce a connection between statistical learning or high-dimensional inference, and models of statistical mechanics in which a large number of elementary units interact with each other in a disordered manner. This relationship is the basis of a vast mathematical program leveraging tools and insights from the physics of disordered systems to improve our understanding of high-dimensional probabilistic models, with applications e.g. in machine learning and constraint satisfaction problems. I will then detail concrete examples of this program by presenting recent advances concerning the phase retrieval problem, as well as a challenging open problem of high-dimensional probability known as the ellipsoid fitting conjecture.
Zoom-Link:
Zoom link and passcode can be found at the Mathematics of Machine Learning and Data Science seminar https://math-ml.univie.ac.at/seminar/