Introduction to High-Dimensional Statistics

Christophe Giraud




Ever-greater computing technologies have given rise to an exponentially growing volume of data. Today massive data sets (with potentially thousands of variables) play an important role in almost every branch of modern human activity, including networks, finance, and genetics. However, analyzing such data has presented a challenge for statisticians and data analysts and has required the development of new statistical methods capable of separating the signal from the noise.

Introduction to High-Dimensional Statistics is a concise guide to state-of-the-art models, techniques, and approaches for handling high-dimensional data. The book is intended to expose the reader to the key concepts and ideas in the most simple settings possible while avoiding unnecessary technicalities.

Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this highly accessible text:

  • Describes the challenges related to the analysis of high-dimensional data
  • Covers cutting-edge statistical methods including model selection, sparsity and the lasso, aggregation, and learning theory
  • Provides detailed exercises at the end of every chapter with collaborative solutions on a wikisite
  • Illustrates concepts with simple but clear practical examples

Introduction to High-Dimensional Statistics is suitable for graduate students and researchers interested in discovering modern statistics for massive data. It can be used as a graduate text or for self-study.