  Methods of high-dimensional probability play a central role in applications
for statistics, signal processing theoretical computer science and related
fields. These lectures present a sample of particularly useful tools of
high-dimensional probability, focusing on the classical and matrix Bernstein's
inequality and the uniform matrix deviation inequality. We illustrate these
tools with applications for dimension reduction, network analysis, covariance
estimation, matrix completion and sparse signal recovery. The lectures are
geared towards beginning graduate students who have taken a rigorous course in
probability but may not have any experience in data science applications.
