Algorithmic High-Dimensional Robust Statistics

This book presents general principles and scalable methodologies to deal with adversarial outliers in high-dimensional datasets.

This reference text offers a clear unified treatment for graduate students, academic researchers, and professionals interested in understanding and developing statistical procedures for high-dimensional data that are robust to idealized modeling assumptions, including robustness to model misspecification and to adversarial outliers in the dataset.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.