Related papers: Lecture notes on high-dimensional data
This text contains lecture notes of the course taught to Ph.D. students of Jagiellonian University in Krakow on 25-28 November, 2013.
Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…
Deep learning (DL) has gained much attention and become increasingly popular in modern data science. Computer scientists led the way in developing deep learning techniques, so the ideas and perspectives can seem alien to statisticians.…
In these lectures I will discuss the following topics: (1) Twistors in 4 flat dimensions: Massless particles; constrained phase space (x,p) versus twistors; Physical states in twistor space. (2) Introduction to 2T-physics and derivation of…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
Citations are the cornerstone of knowledge propagation and the primary means of assessing the quality of research, as well as directing investments in science. Science is increasingly becoming "data-intensive", where large volumes of data…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…
The teaching of statistics in higher education in the UK is still largely lecture-based. This is despite recommendations such as those given by the American Statistical Association's GAISE report that more emphasis should be placed on…
Different sectors have sought to take advantage of opportunities to invest in big data analytics and Natural language processing, in order to improve their productivity and competitiveness. Current challenges facing the higher education…
Data Science is currently a popular field of science attracting expertise from very diverse backgrounds. Current learning practices need to acknowledge this and adapt to it. This paper summarises some experiences relating to such learning…
These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…
This article focuses on how data literacy education such as research data management skills can be integrated into teacher training programmes in order to adequately train the teachers of tomorrow. To this end, interviews were conducted…
This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…
Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic…
Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation…
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…
We present an overview of current academic curricula for Scientific Computing, High-Performance Computing and Data Science. After a survey of current academic and non-academic programs across the globe, we focus on Canadian programs and…