Advanced Topics in Machine Learning: COMPGI13 (kernel part) Arthur Gretton (with Dino Sejdinovic, Steffen Grunewalder)

About

This page will contain slides and detailed notes for the kernel part of the course. I'll also put up the assignments here once they're given out. Note that the slides will be updated as the course progresses, and I modify them to answer questions I get in the classes. I'll put the date of last update next to each document - be sure to get the latest one. Let me know if you find errors.

For questions on the course material, please email Steffen Grunewalder or Dino Sejdinovic.

See David Silver's page for the reinforcement learning part of the course.

Slides and notes

Lectures 1 and 2 slides and notes, last modified 15 Jan 2013

• Definition of a kernel, how it relates to a feature space
• Combining kernels to make new kernels
• The reproducing kernel Hilbert space
• Applications: difference in means, kernel PCA, kernel ridge regression

Lectures 3, 4, 5, 6, and 7 slides and notes, last modified 25 April 2013

• Distance between means in RKHS, integral probability metrics, the maximum mean discrepancy (MMD), two-sample tests
• Choice of kernels for distinguishing distributions, characteristic kernels
• Covariance operator in RKHS: proof of existence, definition of norms (including HSIC, the Hilbert-Schmidt independence criterion)
• Application of HSIC to independence testing
• Application of HSIC to feature selection, taxonomy discovery.
• Introduction to independent component analysis, kernel ICA

Lecture 8 slides and notes, last modified 05 March 2013

• Introduction to convex optimization
• The representer theorem
• Large margin classification, support vector machines for clasification

Lecture 9 slides, lecture 10 slides , and notes, last modified 20 Mar 2013

• Metric, normed, and unitary spaces, Cauchy sequences and completion, Banach and Hilbert spaces
• Bounded linear operators and the Riesz Theorem
• Equivalent notions of an RKHS: existence of reproducing kernel, boundedness of the evaluation operator
• Positive definiteness of reproducing kernels, the Moore-Aronszajn Theorem
• Mercer's Theorem for representing kernels

Supplementary lecture slides, last modified 22 Mar 2012

• Loss and risk, estimation and approximation error, a new interpretation of MMD
• Why use an RKHS: comparison with other function classes (Lipschitz and bounded Lipschitz)
• Characteristic kernels and universal kernels

Assignments

The assignment (first part due in on Friday March 22nd 2013). You will need this extract on incomplete Cholesky (scanned from Shawe-Taylor and Cristianini, Kernel Methods for Pattern Analysis). Last modified 23 Jan 2013.

Contact

arthur.gretton@gmail.com