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Robust Statistics is the study of designing estimators that perform
well even when the dataset significantly deviates from the
idealized modeling assumptions, such as model misspecification or
adversarial outliers in the dataset. The classical statistical
theory, dating back to pioneering works by Tukey and Huber,
characterizes the information-theoretic limits of robust estimation
for most common problems. A recent line of work in computer science
gave the first computationally efficient robust estimators in high
dimensions for a range of learning tasks. This reference text for
graduate students, researchers, and professionals in machine
learning theory, provides an overview of recent developments in
algorithmic high-dimensional robust statistics, presenting the
underlying ideas in a clear and unified manner, while leveraging
new perspectives on the developed techniques to provide streamlined
proofs of these results. The most basic and illustrative results
are analyzed in each chapter, while more tangential developments
are explored in the exercises.
The William Lowell Putnam Mathematics Competition is the most
prestigious undergraduate mathematics problem-solving contest in
North America, with thousands of students taking part every year.
This volume presents the contest problems for the years 2001-2016.
The heart of the book is the solutions; these include multiple
approaches, drawn from many sources, plus insights into navigating
from the problem statement to a solution. There is also a section
of hints, to encourage readers to engage deeply with the problems
before consulting the solutions. The authors have a distinguished
history of engagement with, and preparation of students for, the
Putnam and other mathematical competitions. Collectively they have
been named Putnam Fellow (top five finisher) ten times. Kiran
Kedlaya also maintains the online Putnam Archive.
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