Cambridge Series in Statistical and Probabilistic Mathematics

Cambridge Series in Statistical and Probabilistic Mathematics

Wainwright, Martin J (University of California Berkeley)

Cambridge University Press

02/2019

568

Dura

Inglês

9781108498029

15 a 20 dias

Recent years have seen an explosion in the volume and variety of data collected in scientific disciplines from astronomy to genetics and industrial settings ranging from Amazon to Uber. This graduate text equips readers in statistics, machine learning, and related fields to understand, apply, and adapt modern methods suited to large-scale data.
1. Introduction; 2. Basic tail and concentration bounds; 3. Concentration of measure; 4. Uniform laws of large numbers; 5. Metric entropy and its uses; 6. Random matrices and covariance estimation; 7. Sparse linear models in high dimensions; 8. Principal component analysis in high dimensions; 9. Decomposability and restricted strong convexity; 10. Matrix estimation with rank constraints; 11. Graphical models for high-dimensional data; 12. Reproducing kernel Hilbert spaces; 13. Nonparametric least squares; 14. Localization and uniform laws; 15. Minimax lower bounds; References; Author index; Subject index.