Algorithmic Learning in a Random World / Edition 1

by Vladimir Vovk, Alex Gammerman, Glenn Shafer

Overview

Conformal prediction is a valuable new method of machine learning. Conformal predictors are among the most accurate methods of machine learning, and unlike other state-of-the-art methods, they provide information about their own accuracy and reliability.

This new monograph integrates mathematical theory and revealing experimental work. It demonstrates mathematically the validity of the reliability claimed by conformal predictors when they are applied to independent and identically distributed data, and it confirms experimentally that the accuracy is sufficient for many practical problems. Later chapters generalize these results to models called repetitive structures, which originate in the algorithmic theory of randomness and statistical physics. The approach is flexible enough to incorporate most existing methods of machine learning, including newer methods such as boosting and support vector machines and older methods such as nearest neighbors and the bootstrap.

Topics and Features:
* Describes how conformal predictors yield accurate and reliable predictions, complemented with quantitative measures of their accuracy and reliability

• Handles both classification and regression problems

* Explains how to apply the new algorithms to real-world data sets

• Demonstrates the infeasibility of some standard prediction tasks

* Explains connections with Kolmogorov’s algorithmic randomness, recent work in machine learning, and older work in statistics

• Develops new methods of probability forecasting and shows how to use them for prediction in causal networks

Researchers in computer science, statistics, and artificial intelligence will find the book an authoritative and rigorous treatment of some of the most promising new developments in machine learning. Practitioners and students in all areas of research that use quantitative prediction or machine learning will learn about important new methods.

Product Details

ISBN-13:	9780387001524
Publisher:	Springer US
Publication date:	03/22/2005
Edition description:	2005
Pages:	324
Product dimensions:	6.10(w) x 9.25(h) x 0.03(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 former Dean 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

Preface.- List of Principal results.- Introduction.- 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.- Appendix A: Probability theory.- Appendix B: Data sets.- Appendix C: FAQ.- Notation.- References.- Index

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