High-Dimensional Data Analysis
with Low-Dimensional Models:
Principles, Computation, and Applications
JOHN WRIGHT (Columbia University)
YI MA (University of California, Berkeley)
This material will be published by Cambridge University Press asHigh-Dimensional Data Analysis
with Low-Dimensional Models: Principles, Computation, and Applicationsby John Wright and Yi
Ma. This pre-publication version is free to view and download for personal use only, and is not for
redistribution, re-sale or use in derivative works.
CopyrightãCambridge University Press 2018.
To Mary, Isabella, and Mingshu (J.W.)
To Henry, Barron, and Diana,
and in memory of my father (Y.M.)
Foreword
I recall a moment, perhaps ten or fteen years ago, of prodigious scienti c ac-
tivity. To give our reader a sense of this blessed time, consider a series of regular
scienti c workshops, each involving at most forty participants. Despite the small
size and almost intimate nature of these workshops, they brought together an
energized and enthusiastic mix of people from an array of disciplines, including
mathematics, computer science, engineering, and the life sciences. What a privi-
lege to be in a room with mathematicians such as Terence Tao and Roman Ver-
shynin and learn about high-dimensional geometry; with applied mathematicians
and engineers such as David Donoho, Joel Tropp, Thomas Strohmer, Michael
Elad, and Freddy Bruckstein and learn about the power of algorithms; with sta-
tistical physicists such as Andrea Montanari and learn about phase transitions
in large stochastic systems. What a privilege to learn about fast numerical meth-
ods for large-scale optimization from computer scientists such as Stephen Wright
and Stanley Osher. What a privilege to learn about compressive optical systems
from David Brady and Richard Baraniuk and Kevin Kelly (of single-pixel camera
fame); about compressive analog-to-digital conversion and wideband spectrum
sensing from Dennis Healy, Yonina Eldar, and Azita Emami N
High-Dimensional Data Analysis with Low-Dimensional Models_ Principles, Computation, and Applications_John Wright, Yi Ma.pdf