# Information theory and statistical learning pdf

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Information theory, machine learning and artificial intelligence have been overlapping fields during their whole existence as academic disciplines. These areas, in turn, overlap significantly with applied and theoretical statistics. This course will explore how information-theoretic methods can be used to predict and bound the performance in statistical decision theory and in the process of learning an algorithm from data. The goal is to give PhD students in decision and control, learning, AI, network science, and information theory a solid introduction on how information-theoretic concepts and tools can be applied to problems in statistics, decision and learning well beyond their more traditional use in communication theory. Choose semester and course offering to see information from the correct course syllabus and course offering. Lecture 1: Information theory fundamentals: Entropy, mutual information, relative entropy, and f-divergence.

Machine learning relies heavily on entropy-based e. For instance, Parzen-kernel windows may be used for estimation of various probability density functions, which facilitates the expression of information theoretic concepts as kernel matrices or statistics, e. The parallels between machine learning and information theory allows the interpretation and understand of computational methods from one field in terms of their dual representations in the other. Machine learning ML is the process of data-driven estimation quantitative evidence-based learning of optimal parameters of a model, network or system, that lead to output prediction, classification, regression or forecasting based on a specific input prospective, validation or testing data, which may or may not be related to the original training data. Parameter optimality is tracked and assessed iteratively by a learning criterion depending on the specific type of ML problem. Higher-order learning criteria enable solving problems where sensitivity to higher-moments is important e.

You'll want two copies of this astonishing book, one for the office and one for the fireside at home. NEW for teachers: all the figures available for download as well as the whole book. David J. In this book will be published by CUP. It will continue to be available from this website for on-screen viewing. Notes : Version 6.

## Information Theory and Statistical Learning (eBook, PDF)

Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces Information theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses.

Information theory is the scientific study of the quantification , storage , and communication of information. The field was fundamentally established by the works of Harry Nyquist and Ralph Hartley , in the s, and Claude Shannon in the s. The field is at the intersection of probability theory , statistics , computer science, statistical mechanics , information engineering , and electrical engineering. A key measure in information theory is entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip with two equally likely outcomes provides less information lower entropy than specifying the outcome from a roll of a die with six equally likely outcomes. Some other important measures in information theory are mutual information , channel capacity, error exponents , and relative entropy.

## Information Theory and Statistical Learning

There has been a strong resurgence of AI in recent years. Information theory was first introduced and developed by the great communications engineer, Claude Shannon in the 50's of the last century. The theory was introduced in an attempt to explain the principle behind point-to-point communication and data storing. However, the technique has been incorporated into statistical learning and has inspire many of the underlying principles. In this graduate course, we would try to explore the exciting area of statistical learning from the perspectives of information theorists.

Information Theory and Statistical Learning presents theoretical and practical results about information theoretic methods used in the context of statistical learning.

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