Algorithmic Learning in a Random World

by Vladimir Vovk, Alexander Gammerman, Glenn Shafer

Overview

Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.

Product Details

ISBN-13:	9783031066481
Publisher:	Springer International Publishing
Publication date:	12/14/2022
Edition description:	2nd ed. 2022
Pages:	476
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Vladimir Vovk is Professor of Computer Science at Royal Holloway, University of London. His research interests include machine learning and the foundations of probability and statistics. He was one of the founders of prediction with expert advice, an area of machine learning avoiding making any statistical assumptions about the data. Together with Glenn Shafer and with original inspiration from Philip Dawid, he developed game-theoretic foundations for probability and statistics.

Alexander Gammerman is Professor of Computer Science and co-Director of the Centre for Reliable Machine Learning at Royal Holloway, University of London. His research interests lie in machine learning and pattern recognition, where the majority of his research books, papers, and grants can be found. He is a Fellow of the Royal Statistical Society and has held visiting and honorary professorships from several universities in Europe and the USA.

Glenn Shafer is Professor and formerDean of the Rutgers Business School – Newark and New Brunswick. He is best known for his work in the 1970s and 1980s on the Dempster-Shafer theory, an alternative theory of probability that has been applied widely in engineering and artificial intelligence. Glenn is also known for his initiation, with Vladimir Vovk, of the game-theoretic framework for probability. Their first book on the topic was Probability and Finance: It's Only a Game! A new book on the topic, Game-Theoretic Foundations for Probability and Finance, published in 2019 (Wiley).

Table of Contents

Conformal prediction.- Classification with conformal predictors.- Modifications of conformal predictors.- Probabilistic prediction I: impossibility results.- Probabilistic prediction II: Venn predictors.- Beyond exchangeability.- On-line compression modeling I: conformal prediction.- On-line compression modeling II: Venn prediction.- Perspectives and contrasts.

Editorial Reviews

From the reviews:

"Algorithmic Learning in a Random World has ten chapters, three appendices, and extensive references. Each chapter ends with a section containing comments, historical discussion, and bibliographical remarks. … The material is developed well and reasonably easy to follow … . the text is very readable. … is doubtless an important reference summarizing a large body of work by the authors and their graduate students. Academics involved with new implementations and empirical studies of machine learning techniques may find it useful too." (James Law, SIGACT News, Vol. 37 (4), 2006)

From the Publisher