I have a question about the book "High Dimensional Probability." The book is here, where you can see the topics:
https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf
I am very interested in high dimensional/applied probability with applications to statistical theory/problems.
I was wondering if someone could take a look at the table of contents and tell me if there are active research areas/open problems/famous thesis topics in these subjects? Or is this more of a graduate textbook with well-known results and little to research?
Thank you.
Best Answer
It would be difficult to do research in this area without a solid understanding of many (most?) of the results in that text, and in my opinion this book in particular does a very good job at covering a lot of important results in a clear way. Another book to look at would be Martin Wainwrights High Dimensional Statistics, and Rigollet's High Dimensional Statistics Lecture notes. The Wainwright book does a good job at covering a specific 'research area' in each chapter, for example it has one chapter on sparse linear models, another on sparce PCA, etc, whereas the HDP book covers the fundamentals and has examples in each chapter of applications. I would say both are excellent texts that are good background for any research in high dimensional stats