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Mathematical and Computational Foundations of Learning Theory (Dagstuhl Seminar 15361) Hein, Matthias Lugosi, Gabor Rosasco, Lorenzo learning theory non-smooth optimization (convex and non-convex) signal processing Machine learning has become a core field in computer science. Over the last decade the statistical machine learning approach has been successfully applied in many areas such as bioinformatics, computer vision, robotics and information retrieval. The main reasons for the success of machine learning are its strong theoretical foundations and its multidisciplinary approach integrating aspects of computer science, applied mathematics, and statistics among others. The goal of the seminar was to bring together again experts from computer science, mathematics and statistics to discuss the state of the art in machine learning and identify and formulate the key challenges in learning which have to be addressed in the future. The main topics of this seminar were: - Interplay between Optimization and Learning, - Learning Data Representations. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Matthias Hein and Gabor Lugosi and Lorenzo Rosasco 2016 Is Part Of Dagstuhl Reports, Volume 5, Issue 8 (2016) Article Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagRep.5.8.54 urn:nbn:de:0030-drops-56783 https://drops.dagstuhl.de/entities/document/10.4230/DagRep.5.8.54 eng https://creativecommons.org/licenses/by/3.0/legalcode