Modern information processing and machine learning tasks deal with massive amounts of high-dimensional data with complex correlation structures. The increasing dimensionality of such datasets offers both challenges and benefits. On the one hand, many classical learning and inference methods completely fall apart, as the assumptions they are built on do not take into account the very high-dimensional nature of modern data. On the other hand, unique geometric and probabilistic phenomena, including scaling limits, phase transitions, and universality, emerge in high-dimensional settings. A deeper understanding and clever exploitation of such fascinating (and sometimes counter-intuitive) high-dimensional phenomena can translate to both theoretical breakthroughs and novel algorithms that surpass the current state-of-the-art. Research in this area, which lies at the intersection of statistics, mathematics, computer science, statistical physics, theoretical neural science, and signal processing, has been progressing very rapidly over the past decade.

The goal of this advanced theory-oriented course is to introduce students to fundamental results and recent techniques in high-dimensional probability theory and statistical physics that have been successfully applied to the analysis of information processing and machine learning problems. Discussions will be focused on studying such problems in the high-dimensional limit, on analyzing the emergence of phase transitions, and on understanding the scaling limits of efficient algorithms. This course assumes that students have a solid foundation in undergraduate probability theory (e.g., at the level of Grimmett and Stirzaker). It is designed to be essentially self-contained, with the necessary concepts, tools, algorithms, and rigorous theory developed step-by-step in detailed lectures. Students will be actively engaged, applying what they learn to explore and address research problems of their choice.

This course introduces students to probability theory and statistics, and their applications in engineering. Topics include: randomThis course introduces students to probability theory and statistics, and their applications in network analysis, machine learning, communications, signal processing, imaging and other engineering problems. Topics include: random variables, distributions and densities, conditional expectations, statistical sampling, limit theorems, and Markov chains. The goal of this course is to prepare students with adequate knowledge of probability theory and statistical methods, which will be useful in the study of several advanced undergraduate/graduate courses and in formulating and solving practical engineering problems.