Loss Functions and Their Risks.- Surrogate Loss Functions (*).- Kernels and Reproducing Kernel Hilbert Spaces.- Infinite-Sample Versions of Support VectorMachines.- Basic Statistical Analysis of SVMs.- Advanced Statistical Analysis of SVMs (*).- Support Vector Machines for Classification.- Support Vector Machines for Regression..- Robustness.- Computational Aspects.- Data Mining.
Ingo Steinwart is a researcher in the machine learning group at the Los Alamos National Laboratory. He works on support vector machines and related methods. Andreas Christmann is Professor of Stochastics in the Department of Mathematics at the University of Bayreuth. He works in particular on support vector machines and robust statistics.
From the reviews:“This book has many remarkable qualities which make it commendable to a large mathematical audience. …It is probably the first book on this topic…which is genuinely aimed at a mathematician reader. No technical issue is avoided, and fine points like measurability, integrability, existence and regularity of solutions, etc., are addressed with due rigor and precision. …The authors take special care to make the book self-contained and accessible to non-specialists…always including very detailed proofs for all results. A substantial appendix acts as a handy reference of fundamental results of analysis and probability needed throughout the book, even including a full proof of Talagrand’s concentration inequality. Many well-thought –out exercises very nicely complete each chapter. Finally, the book as a whole, though voluminous and presenting for the most part some very recent results, always stays very coherent to its choices and goals, and obviously a lot of effort has gone into a clear organization of the material. This work is bound to be recognized as a classic reference on this topic.” (MathSciNet)“This book presents an extensive account of … Support Vector Machines (SVMs). … The book has many remarkable qualities which make it commendable to a large mathematical audience. First of all it is probably the first book on this topic … which is genuinely aimed at a mathematician reader. … Secondly, the authors take special care to make the book self contained and accessible to non-specialists … . Many well thought-out exercises very nicely complete each chapter. … a classic reference on this topic.” (Gilles Blanchard, Mathematical Reviews, Issue 2010 f)“A mathematically elaborated topic of support vector machines in a book full with definitions and lemmas. It presents support vector machines (SVMs) as a successful modeling and prediction tool with different examples. This book has 12 chapters and 9 appendices that introduce also marginal applications of SVMs. … This book is … suitable as a textbook on SVMs for graduate courses … .” (Adriana Horníková, Technometrics, Vol. 53 (2), May, 2011)
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