This book constitutes the refereed proceedings of the 19th Annual Conference on Learning Theory, COLT 2006, held in Pittsburgh, Pennsylvania, USA, June 2006.

The book presents 43 revised full papers together with 2 articles on open problems and 3 invited lectures. The papers cover a wide range of topics including clustering, un- and semi-supervised learning, statistical learning theory, regularized learning and kernel methods, query learning and teaching, inductive inference, and more.

This volume contains the papers presented at the 20th International Conference onAlgorithmicLearningTheory(ALT2009), whichwasheldinPorto, Portugal, October 3-5, 2009. The conference was co-located with the 12th International ConferenceonDiscoveryScience (DS 2009). The technicalprogramof ALT 2009 contained 26 papers selected from 60 submissions, and 5 invited talks. The - vited talks were presented during the joint sessions of both conferences. ALT 2009 was the 20th in the ALT conference series, established in Japan in 1990. The series Analogical and Inductive Inference is a predecessor of...

Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in...