Related papers: Lecture notes on high-dimensional data
This paper presents a selective review of statistical computation methods for massive data analysis. A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades. In this work, we focus…
In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
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 describe an introductory data science course, entitled Introduction to Data Science, offered at the University of Illinois at Urbana-Champaign. The course introduced general programming concepts by using the Python programming language…
Big data has now become a strong focus of global interest that is increasingly attracting the attention of academia, industry, government and other organizations. Big data can be situated in the disciplinary area of traditional geospatial…
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…
Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…
Machine learning has been proven to be effective in various application areas, such as object and speech recognition on mobile systems. Since a critical key to machine learning success is the availability of large training data, many…
Large-scale, high-quality data are considered an essential factor for the successful application of many deep learning techniques. Meanwhile, numerous real-world deep learning tasks still have to contend with the lack of sufficient amounts…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…
Introduction: Even in effectively conducted randomised trials, the probability of a successful study remains relatively low. With recent advances in the next-generation sequencing technologies, there is a rapidly growing number of…
Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…
The proliferation of vast quantities of available datasets that are large and complex in nature has challenged universities to keep up with the demand for graduates trained in both the statistical and the computational set of skills…
Emphasis is on 2d target space (c=1 coupled to gravity). Contents: 0. Introduction, Overview, and Purpose 1. Loops and States in Conformal Field Theory 2. 2D Euclidean Quantum Gravity I: Path Integral Approach 3. Brief Review of the…
This in an introduction to random matrix theory, giving an impression of some of the most important aspects of this modern subject. In particular, it covers the basic combinatorial and analytic theory around Wigner's semicircle law,…
Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…