Andrea Montanari

The classical statistical estimation problem requires to reconstruct an unknown vector of parameters from a set of observations, when the two are connected through a stochastic relationship. Over the last ten years, a whole new generation of...

Starting in the 70's, physicists have introduced a class of random energy functions and corresponding random probability distributions (Gibbs measures), the are known as mean-field spin glasses. Over the years, it has become increasingly clear that a...

Lecture 2) Message passing algorithms and approximate message passing (AMP). Sharp analysis of AMP. This is a continuation of the first lecture given on Monday. See here for more details

Lecture 3) Optimal AMP algorithms. Connection with Bayes error. Connection with convex optimization. This is a continuation of the first lecture given on Monday. See here for more details

Lecture 4) Replica symmetry breaking. Parisi formula. Computational implications aspect. This is a continuation of the first lecture given on Monday. See here for more details

Lecture 5) Optimization algorithms for mean field spin glasses. This is a continuation of the first lecture given on Monday. See here for more details

Random high-dimensional cost functions and random probability distributions arise in a number of applied fields. For instance, in high-dimensional statistics, an M-estimator is the solution of a random optimization problem (the randomness being...