Algorithmic High-Dimensional Robust Statistics

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

Ilias Diakonikolas (Author), Daniel M. Kane (Author)

9781108837811, Cambridge University Press

Hardback, published 7 September 2023

300 pages
23.6 x 15.8 x 2.2 cm, 0.58 kg

'This volume was designed as a graduate textbook for a one-semester course, but it could also be useful for researchers and professionals in machine learning. While the foundational knowledge in computer science and statistics required is high, certain upper-level undergraduates could start their studies here. … Recommended.' J. J. Meier, Choice

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.

1. Introduction to robust statistics
2. Efficient high-dimensional robust mean estimation
3. Algorithmic refinements in robust mean estimation
4. Robust covariance estimation
5. List-decodable learning
6. Robust estimation via higher moments
7. Robust supervised learning
8. Information-computation tradeoffs in high-dimensional robust statistics
A. Mathematical background
References
Index.

Subject Areas: Pattern recognition [UYQP]