Diakonikolas I. Algorithmic High-Dimensional Robust Statistics 2023 torrent

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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 in the presence of 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 book is intended as an introduction to the field of algorithmic robust statistics, and is suitable as a graduate text for a one-semester course. The reader is assumed to have an understanding of algorithms at the undergraduate level, including basic knowledge of convex programming techniques, as well as a solid background in linear algebra and probability theory. Beyond these topics, the book is intended to be largely self-contained, with background on a few mathematical topics included in the Appendix.
Throughout this book, we have so far focused on robust algorithms for Unsupervised Learning problems, that is, problems about learning some parameters like the mean or covariance of a distribution. In this chapter, we illustrate how the algorithmic ideas developed in this book can be applied to supervised problems as well. At a high level, Supervised Learning is the task of inferring a function from a set of labeled observations.
Preface
Introduction to Robust Statistics
Efficient High-Dimensional Robust Mean Estimation
Algorithmic Refinements in Robust Mean Estimation
Robust Covariance Estimation
List-Decodable Learning
Robust Estimation via Higher Moments
Robust Supervised Learning
Information-Computation Trade-offs in High-Dimensional Robust Statistics
Appendix Mathematical Background