Geometry and Statistics

As massive and complex datasets are now much more prevalent, it has become necessary to understand the underlying geometric structure of the data for reliable statistical inference. This monograph will give a comprehensive and systematic overview of the role of geometry in statistics. It covers three broad modern topics: data geometry, learning geometry (high dimensional inference), and information geometry. The book includes lots of examples to illustrate the methods, and R code for their implementation. The book should be a useful reference for researchers and graduate students in statistics and machine learning with a good background in mathematics.