Syllabus : Introduction: Data representation, similarity, statistical learning theory, hyper-plane classifiers, support vector classification, support vector regression, kernel principal component analysis Kernels: Product features, representation of similarities in linear spaces, examples and properties of kernels Risk and loss functions: Loss functions, test error, expected risk, statistical perspective, robust estimators Regularization: Regularized risk functional, representer theorem, regularization operators, translation invariant kernels, dot product kernels Optimization: Convex optimization, unconstrained problems, constrained problems Support vector machines: Separating hyper-planes, role of margin, optimal margin hyper-planes, nonlinear support vector classifiers, soft margin hyper-planes, multi-class hyper-planes Single class problems: introduction, algorithms, optimization, theory Regression estimation: Linear regression with insensitive loss function, dual problems, $\nu$-SV regression Implementation: Tricks of the trade, sparse greedy matrix approximation, subset selection methods, sequential minimal optimization, iterative methods Designing kernels: Tricks for constructing kernels, string kernels, natural kernels. |
Texts : 1. Bernhard Schlkopf and Alexander J. Smola. Learning with Kernels - support vector machines, regularization, optimization and beyond, The MIT Press, Cambridge, Massachusetts, London, England, 2002. |
References : 1. John Shawe-Taylor and Nello Cristianini, Kernel Methods for Pattern Analysis, Cambridge University Press, 2004. 2. Nello Cristianini and John Shawe-Taylor , Introduction to Support Vector Machines, Cambridge University Press, 2000. |