ITS Seminar with Stefano Sarao Minelli
MAR 06, 2020 | 2:00 PM TO 3:00 PM
The Graduate Center
365 Fifth Avenue
March 06, 2020: 2:00 PM-3:00 PM
Initiative for the Theoretical Sciences
Stefano Sarao Minelli (Saclay/Courant) gives a seminar titled "Thresholds of descending algorithms in inference problems" at the Initiative for the Theoretical Sciences in Room 5209.
In problems characterized by numerous degrees of freedom many relevant observables require the evaluation of prohibitive high-dimensional integrals. In general, we rely on two strategies to perform such computations: we consider dynamics that asymptotically characterize the integral; or we approximate the integral reducing the degrees of freedom. In particular I will consider the Langevin algorithm and a variation of cavity method. I will discuss a prototypical model from statistical inference where both the approaches can be analyzed. Using tools from the statistical physics of disordered systems I will draw a phase diagram of the algorithms and explain why and when they fail. Finally, I will extend the analysis to gradient descent algorithm and highlight aspects of interest in machine learning problems.