Statistical Learning Theory and Applications

Explore the mathematical foundations of machine learning through this comprehensive graduate-level course covering statistical learning theory and its practical applications. Delve into fundamental concepts starting with the learning problem and regularization techniques, then progress through reproducing kernel Hilbert spaces, positive definite functions, and feature maps. Master essential algorithms including logistic regression, support vector machines, and regularized least squares while understanding the theoretical underpinnings of Tikhonov regularization and the representer theorem. Learn advanced optimization techniques such as iterative regularization via early stopping, stochastic gradient methods, and large-scale kernel methods. Examine sparsity-based regularization approaches including convex relaxation, proximal gradient methods, and structured sparsity regularization. Investigate multiple kernel learning frameworks and dive deep into learning theory fundamentals covering generalization error, stability analysis, and modern deep learning optimization theory. Gain both theoretical insights and practical skills needed to understand and apply state-of-the-art machine learning methods across various domains.