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.