Statistical learning without probabilistic assumption?

Readings

Books and Lecture Notes

• Nicolò Cesa-Bianchi and Gábor Lugosi, Prediction, Learning, and Games, Cambridge University Press, 2006.

  This book offers the first comprehensive treatment of the problem of predicting “individual sequences”. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class.

• STAT928@Wharton, UPenn: Statistical Learning Theory and Sequential Prediction. This is a course taught by Alexander Rakhlin and Karthik Sridharan, focusing on theoretical aspects of Statistical Learning and Sequential Prediction, with comprehensive and constantly evolving lecture notes. There is also a list of suggested readings on the webpage of the course.

Articles, Essays and Papers

• Statistics without Probability (Individual Sequences): A blog post by Larry Wasserman giving a brief introduction to this topic, and some important references.