Information Theoretic Methods In Data Science

The first unified treatment of the interface between information theory and emerging topics in data science, written in a clear, tutorial style. Covering topics such as data acquisition, representation, analysis, and communication, it is ideal for graduate students and researchers in information theory, signal processing, and machine learning.

This interdisciplinary text offers theoretical and practical results of information theoretic methods used in statistical learning. It presents a comprehensive overview of the many different methods that have been developed in numerous contexts.

"Information Theory and Statistical Learning" presents theoretical and practical results about information theoretic methods used in the context of statistical learning. The book will present a comprehensive overview of the large range of different methods that have been developed in a multitude of contexts. Each chapter is written by an expert in the field. The book is intended for an interdisciplinary readership working in machine learning, applied statistics, artificial intelligence, biostatistics, computational biology, bioinformatics, web mining or related disciplines. Advance Praise for "Information Theory and Statistical Learning": "A new epoch has arrived for information sciences to integrate various disciplines such as information theory, machine learning, statistical inference, data mining, model selection etc. I am enthusiastic about recommending the present book to researchers and students, because it summarizes most of these new emerging subjects and methods, which are otherwise scattered in many places." Shun-ichi Amari, RIKEN Brain Science Institute, Professor-Emeritus at the University of Tokyo

Understand key information-theoretic principles that underpin the design of next-generation cellular systems with this invaluable resource. This book is the perfect tool for researchers and graduate students in the field of information theory and wireless communications, as well as for practitioners in the telecommunications industry.

Table of contents

The aim of this book is to provide an internationally respected collection of scientific research methods, technologies and applications in the area of data science. This book can prove useful to the researchers, professors, research students and practitioners as it reports novel research work on challenging topics in the area surrounding data science. In this book, some of the chapters are written in tutorial style concerning machine learning algorithms, data analysis, information design, infographics, relevant applications, etc. The book is structured as follows: • Part I: Data Science: Theory, Concepts, and Algorithms This part comprises five chapters on data Science theory, concepts, techniques and algorithms. • Part II: Data Design and Analysis This part comprises five chapters on data design and analysis. • Part III: Applications and New Trends in Data Science This part comprises four chapters on applications and new trends in data science.

This book is the first cohesive treatment of ITL algorithms to adapt linear or nonlinear learning machines both in supervised and unsupervised paradigms. It compares the performance of ITL algorithms with the second order counterparts in many applications.

Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC