Reproducing Kernel Hilbert Space and Applications

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Topics and Objectives

• Functional approximation basics
• Reproducing kernel Hilbert space (RKHS) and the kernel trick
• Representer theorem and its applications
• Kernel ridge regression
• Support vector machines and regression
• Kernel PCA
• Kernel mean embedding

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Week 1 (Aug 26 and Aug 28)

• Aug 26: [Course Introduction and Overview]
• Aug 26: [Functional Approximation: some motivating examples]
• Aug 28: [Smoothing splines and the choice of knots] [R Code and Additional Examples] [Source Code]

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Homework 1

• [Homework 1] [Source Code]
• Due Sep 10, 11:59PM CT

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Week 2 (Sep 2 and Sep 4)

• Sep 2: [RKHS and Kernel Functions]
• Sep 4: [Kernel Ridge Regression]

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Week 3 (Sep 9 and Sep 11)

• Homework 1 Due (Sep 10)
• Sep 9: [The Rrepresenter Theorem]
• Sep 11: [Support Vector Machines] [Support Vector Regression]

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Week 4 (Sep 16 and Sep 18)

• Sep 16: [Kernel PCA]
• Sep 18: [Kernel Mean Embedding]

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Homework 2

• [Homework 2] [Source Code]
• Due Sep 24, 11:59PM CT

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