`p-Norm Multiple Kernel Learning
Making Learning with Multiple Kernels Effective
`p-Norm Multiple Kernel Learning
vorgelegt von Dipl.-Math.
Marius Kloft
Von der Fakult¨at IV - Elektrotechnik und Informatik
der Technischen Universit¨at Berlin zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
– Dr. rer. nat. –
genehmigte
Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Manfred Opper
Fakult¨at IV – Elektrotechnik und Informatik
Technische Universit¨at Berlin
Berichter: Prof. Dr. Klaus-Robert M¨uller
Fakult¨at IV – Elektrotechnik und Informatik
Technische Universit¨at Berlin
Prof. Dr. Peter L. Bartlett
Department of EECS and Department of Statistics
University of California, Berkeley, USA
Prof. Dr. Gilles Blanchard
Institut f¨ur Mathematik
Universit¨at Potsdam
Tag der m¨undlichen Aussprache: 26.09.2011
Berlin, 2011
D 83
To my parents
Acknowledgements
I am deeply grateful for the opportunity to have worked with so many brilliant and
creative minds over the last years. First of all, I would like to thank my PhD advisors
Prof. Dr. Klaus-Robert M¨uller, Prof. Dr. Peter L. Bartlett, and Prof. Dr. Gilles
Blanchard. Of course, I owe the utmost gratitude to Professor M¨uller, who initially
introduced me to the subject of machine learning in 2007; with his infectious optimism,
wit, and curiosity, he created the open and stimulating atmosphere that characterizes
his Machine Learning Laboratory at TU Berlin. It was also Professor M¨uller who gave
me advice and support in various respects from the very beginning of my PhD studies,
thus turning out to be much more than just a scientific advisor. I am deeply thankful
to him. By the same token, I would like to thank all members of his lab for creating
such a pleasurable working atmosphere in the office each day, most notably my former
and current office mates Pascal Lehwark, Nico G¨ornitz, Gregoire Montavon, and Stefan
Haufe.
Furthermore, I would like to thank Professor Bartlett very much indeed for kindly
inviting me over to visit his learning theory group at UC Berkeley, a most enjoyable and
inspiring experience in many ways, and, most of all, for introducing me to the fascinat-
ing world of learning theory; his readiness to share his vast knowledge with me allowed
me to gain a deeper understanding of the field. I also thank all members of his group,
especially Alekh, for our stimulating discussions, not limited to
various mathematical subjects, but also in matters of the every-
day life. I also thank all office mates in Sutardja Dai Hall for
the nice atmosphere, and the UC Berkeley for providing such a
great office with an absolutely stunning view of the SF Bay, all of
which contributed to making my stay (Oct 2009–Sep 2010) such
a memorable one.
Likewise, I am very grateful to Professor Blanchard for taking so much of his valu-
able time for our extensive and fruitful discussions on various mathematical problems,
sharing his immense knowledge and deep insights with me. I remember us sitting in
caf´es for hours, trying to solve a mathematical puzzle arising from our joint research
III
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