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 16th Annual International Conference on Algorithmic Learning Theory (ALT 2005), which was held in S- gapore (Republic of Singapore), October 8-11, 2005. The main objective of the conference is to provide an interdisciplinary forum for the discussion of the t- oretical foundations of machine learning as well as their relevance to practical applications. The conference was co-located with the 8th International Conf- enceonDiscoveryScience(DS2005). Theconferencewasalsoheldinconjunction with the centennial celebrations of the National University of Singapore. The volume includes 30 technical contributions, which were selected by the program committee from 98 submissions. It also contains the ALT 2005 invited talks presented by Chih-Jen Lin (National Taiwan University, Taipei, Taiwan) on "Training Support Vector Machines via SMO-type Decomposition Methods," and by Vasant Honavar (Iowa State University, Ames, Iowa, USA) on "Al- rithmsandSoftwareforCollaborativeDiscoveryfromAutonomous, Semantically Heterogeneous, Distributed, Information Sources. " Furthermore, this volume - cludes an abstract of the joint invited talk with DS 2005 presented by Gary L. Bradshaw (Mississippi State University, Starkville, USA) on "Invention and Arti?cial Intelligence," and abstracts of the invited talks for DS 2005 presented by Ross D. King (The University of Wales, Aberystwyth, UK) on "The Robot Scientist Project," and by Neil Smalheiser (University of Illinois at Chicago, Chicago, USA) on "The Arrowsmith Project: 2005 Status Report. " The c- plete versions of these papers are published in the DS 2005 proceedings (Lecture Notes in Computer Science Vol. 3735).

This book constitutes the refereed proceedings of the 27th International Conference on Algorithmic Learning Theory, ALT 2016, held in Bari, Italy, in October 2016, co-located with the 19th International Conference on Discovery Science, DS 2016. The 24 regular papers presented in this volume were carefully reviewed and selected from 45 submissions. In addition the book contains 5 abstracts of invited talks. The papers are organized in topical sections named: error bounds, sample compression schemes; statistical learning, theory, evolvability; exact and interactive learning; complexity of teaching models; inductive inference; online learning; bandits and reinforcement learning; and clustering.

Eine der wichtigsten Grundlagen der Technik ist die Mathematik. Ziel der Techniker- und Ingenieurausbildung muB es daher u. a. sein, mathematische Kenntnisse in einem solchen AusmaB zu vermitteln, daB der Studierende alie an ihn herantretenden mathematischen Probleme sicher meistern kann. Dazu ist es notig, diese Kenntnisse so aufzunehmen und geistig zu verarbeiten, daB sich mathematische Fahigkeiten und Fertigkeiten entwickeln, die ein selbstandiges mathematisches Denken und Arbeiten ermoglichen. Die rasante Entwicklung von Technik und Wirtschaft bringt es mit sich, daB der Umfang der mathematischen Wissenschaft und damit auch die Fiilie des vom Stu- dierenden aufzunehmenden Stoffes standig wachst. Stoffkomplexe, mathematische Begriffe, Rechenverfahren usw., die noch vor nicht allzu langer Zeit Aufgabe eines Spezialstudiums im fortgeschrittenen Ausbildungsstadium waren, gehoren heute zu den selbstverstandlichen Grundlagen einer jeden mathematischen Ausbildung. Damit den Lernenden die Fiille des Stoffes nicht erdriickt, ist es heute mehr denn je notig, a) eine strenge Stoffauswahl zu treffen, b) den dargebotenen Stoff denkend zu erfassen und nicht nur anzulernen, c) daS erworbene Wissen und die entwickelten Fahigkeiten durch hinreichende und klug ausgewahlte tTbungen fiir die Praxis anwendungsbereit zu machen und zu erhalten. Nur eine solche rationalisierte Ausbildung kann heute und kiinftig noch greifbare Erfolge gewahrleisten.