Kernel Methods in Machine Learning: Kernel Regression and SVM

This lecture covers kernel methods in machine learning, focusing on kernel regression and support vector machines (SVM). It begins with the Representer theorem, which allows kernelizing linear regression by expressing the solution as a linear combination of training samples. The instructor explains the kernel function and its role in measuring similarity between samples, leading to the formulation of the kernel matrix. The lecture details the process of kernel regression, including the empirical risk minimization and the gradient descent approach to find optimal parameters. The discussion extends to kernel ridge regression, emphasizing the importance of regularization to prevent overfitting. The instructor also demonstrates how to compute predictions using kernel functions without explicitly defining the feature mapping. The lecture concludes with examples of kernel SVM, illustrating how kernel methods can be applied to both linear and non-linear classification problems, and the impact of hyperparameters on model performance. Overall, the lecture provides a comprehensive overview of kernel methods and their applications in machine learning.