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.

This book is about conformal prediction, an approach to prediction that originated in machine learning in the late 1990s. The main feature of conformal prediction is the principled treatment of the reliability of predictions. The prediction algorithms described — conformal predictors — are provably valid in the sense that they evaluate the reliability of their own predictions in a way that is neither over-pessimistic nor over-optimistic (the latter being especially dangerous). The approach is still flexible enough to incorporate most of the existing powerful methods of machine learning. The book covers both key conformal predictors and the mathematical analysis of their properties. Algorithmic Learning in a Random World contains, in addition to proofs of validity, results about the efficiency of conformal predictors. The only assumption required for validity is that of "randomness" (the prediction algorithm is presented with independent and identically distributed examples); in later chapters, even the assumption of randomness is significantly relaxed. Interesting results about efficiency are established both under randomness and under stronger assumptions. Since publication of the First Edition in 2005 conformal prediction has found numerous applications in medicine and industry, and is becoming a popular machine-learning technique. This Second Edition contains three new chapters. One is about conformal predictive distributions, which are more informative than the set predictions produced by standard conformal predictors. Another is about the efficiency of ways of testing the assumption of randomness based on conformal prediction. The third new chapter harnesses conformal testing procedures for protecting machine-learning algorithms against changes in the distribution of the data. In addition, the existing chapters have been revised, updated, and expanded.

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.

This volume contains the papers presented at the 21st International Conf- ence on Algorithmic Learning Theory (ALT 2010), which was held in Canberra, Australia, October 6–8, 2010. The conference was co-located with the 13th - ternational Conference on Discovery Science (DS 2010) and with the Machine Learning Summer School, which was held just before ALT 2010. The tech- cal program of ALT 2010, contained 26 papers selected from 44 submissions and ?ve invited talks. The invited talks were presented in joint sessions of both conferences. ALT 2010 was dedicated to the theoretical foundations of machine learning and took place on the campus of the Australian National University, Canberra, Australia. ALT provides a forum for high-quality talks with a strong theore- cal background and scienti?c interchange in areas such as inductive inference, universal prediction, teaching models, grammatical inference, formal languages, inductive logic programming, query learning, complexity of learning, on-line learning and relative loss bounds, semi-supervised and unsupervised learning, clustering,activelearning,statisticallearning,supportvectormachines,Vapnik- Chervonenkisdimension,probablyapproximatelycorrectlearning,Bayesianand causal networks, boosting and bagging, information-based methods, minimum descriptionlength,Kolmogorovcomplexity,kernels,graphlearning,decisiontree methods, Markov decision processes, reinforcement learning, and real-world - plications of algorithmic learning theory. DS 2010 was the 13th International Conference on Discovery Science and focused on the development and analysis of methods for intelligent data an- ysis, knowledge discovery and machine learning, as well as their application to scienti?c knowledge discovery. As is the tradition, it was co-located and held in parallel with Algorithmic Learning Theory.

This unique volume is an introduction for computer scientists, including a formal study of theoretical algorithms for Big Data applications, which allows them to work on such algorithms in the future. It also serves as a useful reference guide for the general computer science population, providing a comprehensive overview of the fascinating world of such algorithms.To achieve these goals, the algorithmic results presented have been carefully chosen so that they demonstrate the important techniques and tools used in Big Data algorithms, and yet do not require tedious calculations or a very deep mathematical background.

This book constitutes the proceedings of the 25th International Conference on Algorithmic Learning Theory, ALT 2014, held in Bled, Slovenia, in October 2014, and co-located with the 17th International Conference on Discovery Science, DS 2014. The 21 papers presented in this volume were carefully reviewed and selected from 50 submissions. In addition the book contains 4 full papers summarizing the invited talks. The papers are organized in topical sections named: inductive inference; exact learning from queries; reinforcement learning; online learning and learning with bandit information; statistical learning theory; privacy, clustering, MDL, and Kolmogorov complexity.