This is a theoretical course about probability in high dimensions. We will look at some mathematical phenomena appearing as the number of random variables grows large - e.g. concentration of measure or universality. ...
A rigorous introduction to the statistical analysis of random functions and associated random operators. Viewing random functions either as random Hilbert vectors or as stochastic processes, we will see the interplay between nonparametrics and multivariate ...
This is an introductory course to the concentration of measure phenomenon - random functions that depend on many random variables tend to be often close to constant functions. ...
Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, with an application oriented approach and hands-on numeri ...
Introduction to the physics of random processes and disordered systems, providing an overview over phenomena, concepts and theoretical approachesTopics include:
Random walks; Roughening/pinning; Localization; Random matrix theory; Spin glasses; Disorder ...
This course aims to provide graduate students a thorough grounding in the methods, theory, mathematics and algorithms needed to do research and applications in machine learning. The course covers topics from machine learning, classical statistics, and data ...
Information-theoretic methods and their application to secrecy & privacy. Perfect information-theoretic secrecy. Randomness extraction & privacy amplification. Secret key generation from common randomness. Measures of information leakage incl. differential ...
This class will introduce quantum chaos and it's connection to black holes and quantum gravity. We will first review chaos in classical mechanics, before turning to semi-classical chaos and random matrix theory, thermalization and the Eigenstate Thermaliza ...