Algorithmic Learning in a Random World

1. Front Matter

   Pages I-XV

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2. Introduction

   Pages 1-15

3. Conformal prediction

   Pages 17-51

4. Classification with conformal predictors

   Pages 53-96

5. Modifications of conformal predictors

   Pages 97-130

6. Probabilistic prediction I: impossibility results

   Pages 131-142

7. Probabilistic prediction II: Venn predictors

   Pages 143-168

8. Beyond exchangeability

   Pages 169-187

9. On-line compression modeling I: conformal prediction

   Pages 189-221

10. On-line compression modeling II: Venn prediction

    Pages 223-240

11. Perspectives and contrasts

    Pages 241-273

12. Back Matter

    Pages 275-324

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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.

• Approximation
• Conformal prediction
• Randomness
• Regression
• algorithms
• classification
• learning
• machine learning
• modeling

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)

• Computer Learning Research Centre, Dept. of Computer Science Royal Holloway, University of London, Egham Surrey, UK

  Vladimir Vovk, Alexander Gammerman

• Dept. of Accounting and Information Systems Rutgers Business School, Newark and New Brunswick, Newark

  Glenn Shafer

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