09 — Kernel Methods and RKHS¶
This module provides a rigorous exploration of Kernel Methods and Reproducing Kernel Hilbert Spaces (RKHS). We transition from simple linear classifiers to infinite-dimensional feature spaces, covering the functional analytic foundations that make these methods both powerful and theoretically elegant.
Prerequisite Tier: Tier 2 — Intermediate (Requires Linear Algebra, Multivariable Calculus, and basic Functional Analysis)
📚 Course Modules¶
- Lecture: Unified Mathematical Foundations
- Practice: Exercises and Coding Tasks
- Project: Scaling Kernels with RFF and Nyström
📄 Core Literature¶
- Schölkopf, B., & Smola, A. J. (2002): Learning with Kernels - The definitive textbook on kernel methods.
- Rahimi, A., & Recht, B. (2007): Random Features for Large-Scale Kernel Machines - The paper that enabled kernels to scale to massive datasets.
- Muandet, K., et al. (2017): Kernel Mean Embedding of Distributions: A Review and Beyond - Foundations of MMD and distribution embeddings.
- Aronszajn, N. (1950): Theory of Reproducing Kernels - The original work on RKHS.