Algorithmic Learning in a Random World

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).

• 1. Introduction.- Part I Set prediction.- 2. Conformal prediction: general case and regression.- 3. Conformal prediction: classification and general case.- 4. Modifications of conformal predictors.- Part II Probabilistic prediction.- 5. Impossibility results.- 6. Probabilistic classification: Venn predictors.- 7. Probabilistic regression: conformal predictive systems.- Part III Testing randomness.- 8. Testing exchangeability.- 9. Efficiency of conformal testing.- 10. Non-conformal shortcut.- Part IV Online compression modelling.- 11. Generalized conformal prediction.- 12. Generalized Venn prediction and hypergraphical models.- 13. Contrasts and perspectives.