Related papers: High-Dimensional Statistics
These are lecture notes for a one semester introductory course I gave at Indiana University. The goal was to make this exposition as clear and elementary as possible. A particular emphasis is given on examples involving SU(1,1). These notes…
Data-driven decision making is serving and transforming education. We approached the problem of predicting students' performance by using multiple data sources which came from online courses, including one we created. Experimental results…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
In this thesis I develop a variety of techniques to train, evaluate, and sample from intractable and high dimensional probabilistic models. Abstract exceeds arXiv space limitations -- see PDF.
Over 1100 students over four semesters were given the option of taking an introductory undergraduate statistics class either by in-person attendance in lectures or by taking exactly the same class (same instructor, recorded lectures,…
This Chapter, "High-dimensional ABC", is to appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and concepts behind extending ABC methods to higher dimensions, with supporting examples…
This study examined the teaching practices of 227 college instructors of introductory statistics (from the health and behavioral sciences). Using primarily multidimensional scaling (MDS) techniques, a two-dimensional, 10-item teaching…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…
The second part of a set of notes based on lectures given at the IHES in 2015 on Feynman amplitudes and motivic periods.
The undergraduate curriculum in statistics and data science is undergoing changes to accommodate new methods, newly interested students, and the changing role of statistics in society. Because of this, it is more important than ever that…
Clinical notes contain information about patients that goes beyond structured data like lab values and medications. However, clinical notes have been underused relative to structured data, because notes are high-dimensional and sparse. This…
Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and…
In change-point analysis, one aims at finding the locations of abrupt distributional changes (if any) in a sequence of multivariate observations. In this article, we propose some nonparametric methods based on averages of pairwise distances…
The probabilistic investigation on record values and record times of a sequence of random variables defined on the same probability space has received much attention from 1952 to now. A great deal of such theory focused on \textit{iid} or…
These are lecture notes of the course in infinity categories given in the fall 2016 at Weizmann Institute.
These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as…
We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from $L_p$ norms whose behavior is similar under $H_0$ but potentially different…
The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now is growing at a healthy rate. This chapter, for the {\it Highly Structured Stochastic Systems} book (Oxford University Press, 2003)…
Instructors of statistics who teach non-statistics majors possess varied academic backgrounds, and hence it is reasonable to expect variability in their content knowledge, and pedagogical approach. The aim of this study was to determine the…
These are the notes of the three lectures I delivered at the mini-workshop "Knot Theory and Number Theory around the A-Polynomial" at the Instituto Superior Tecnico (IST) in Lisbon in January 2014. The goal of the lectures was to…