Advances in Learning Theory: Methods, Models, and ApplicationsJohan A. K. Suykens In recent years, considerable progress has been made in the understanding of problems of learning and generalization. In this context, intelligence basically means the ability to perform well on new data after learning a model on the basis of given data. Such problems arise in many different areas and are becoming increasingly important and crucial towards many applications such as in bioinformatics, multimedia, computer vision and signal processing, internet search and information retrieval, datamining and textmining, finance, fraud detection, measurement systems, process control and several others. Currently, the development of new technologies enables to generate massive amounts of data containing a wealth of information that remains to become explored. Often the dimensionality of the input spaces in these novel applications is huge. This can be seen in the analysis of micro-array data, for example, where expression levels of thousands of genes need to be analyzed given only a limited number of experiments. Without performing dimensionality reduction, the classical statistical paradigms show fundamental shortcomings at this point. Facing these new challenges, there is a need for new mathematical foundations and models in a way that the data can become processed in a reliable way. The subjects in this publication are very interdisciplinary and relate to problems studied in neural networks, machine learning, mathematics and statistics. |
Contents
An Overview of Statistical Learning Theory | 1 |
An Optimization Perspective on Kernel Partial Least Squares Regres | 11 |
Cucker Smale Learning Theory in Besov Spaces | 53 |
32 | 60 |
47 | 70 |
Functional Learning through Kernels | 89 |
Leaveoneout Error and Stability of Learning Algorithms with | 111 |
Regularized LeastSquares Classification | 131 |
Bayesian Regression and Classification | 267 |
from Likelihood Fields to Hyperfields | 289 |
90 | 311 |
R Kulhavý | 312 |
Bayesian Smoothing and Information Geometry | 321 |
Györfi D Schäfer | 332 |
Nonparametric Prediction | 341 |
Recent Advances in Statistical Learning Theory | 357 |
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Advances in Learning Theory: Methods, Models, and Applications Johan Suykins No preview available - 2003 |
Common terms and phrases
algorithm analysis applications approach approximation basis functions Bayesian binary bound classification consider constraints construct convergence convex data points dataset defined denote derived dimensional documents dual empirical error empirical risk equation example feature space finite formulation Gaussian processes given Hilbert space hyperfields hyperparameters hyperplane hypothesis IEEE indicator functions inequality input J.A.K. Suykens K-PLS kernel function kernel matrix kernel PCA learning algorithm learning machine least squares leave-one-out error likelihood linear loss function LS-SVM Machine Learning mapping margin minimization multiclass Neural Networks nonlinear norm obtained operator optimal output parameter posterior prediction prior probability measure problem random regularization representation reproducing kernel risk functional RLSC samples Schölkopf semantic Smola solution solving stability Statistical Learning Theory subset support vector machines Theorem training data training set v-SVM Vapnik VC dimension VC-dimension zero