Probabilistic Tools in Large Matrix Estimation

NB: cours de 3h dans le cadre de la journée 

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We will discuss several problems related to estimation of large matrices including low rank matrix recovery, trace regression and covariance estimation. The main focus will be on probabilistic tools needed to provide sharp nonasymptotic bounds on the estimation error in relevant norms in the spaces of matrices (such as the operator norm, the Hilbert--Schmidt norm, etc). These tools include probabilistic inequalities for sums of independent random matrices (such as, for instance, noncommutative Bernstein type inequalities) as well as more general concentration inequalities and moment bounds for empirical processes. The course is aimed at PhD students in disciplines such as mathematical optimization, machine learning, computer science, statistics, applied mathematics and engineering. However, it is also suitable to researchers in various quantitative disciplines interested in the topic.