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SCHEDULE
Lecturers:
BS: Bernhard Schölkopf
NL: Neil Lawrence
MG: Mark Girolami
FPC: Fernando Perez-Cruz
RV: Robert Vanderbei
ZG: Zoubin Ghahramani
PO: Peter Orbanz
GL: Gabor Lugosi
JC: John Cunningham
DG: Dilan Gorur
Titles and abstracts of courses
Kernel Methods
Bernhard Schölkopf, Max Plank Institute Tübingen
The course will cover some basic ideas of learning theory, elements of the theory of reproducing kernel Hilbert spaces, and some machine learning algorithms that build upon this.
Concentration inequalities in machine learning
Gabor Lugosi, Universitat Pompeu Fabra
In the analysis of machine learning algorithms one often faces
complicated functions of many independent random variables. In such situations concentration
inequalities, that quantify the size of typical deviations of such functions from
their expected value, offer an elegant and versatile tool. The theory of concentration
inequalities has seen spectacular advance in the last few decades. These inequalities proved
to be useful not only in machine learning but also in a wide variety of areas,
including combinatorics, graph theory, analysis of algorithms. information theory, geometry, just to
name a few. This course offers an introduction to the theory and a summary of some of
the most useful results with a sample of illustrations of their use in learning theory.
Diffusions and Geodesic Flows on Manifolds: The Differential Geometry of Markov Chain Monte Carlo
Mark Girolami, University College London
Markov Chain Monte Carlo methods provide the most comprehensive set of simulation based tools to enable inference over many classes of statistical models. The complexity of many applications presents an enormous challenge for sampling methods motivating continual innovation in theory, methodology and associated algorithms. In this series of lectures we will consider one recent advance in MCMC methodology, that has exploited mathematical ideas from differential geometry, classical nonlinear dynamics, and diffusions constrained on manifolds, in attempting to provide the tools required to attack some of the most challenging of sampling problems presented to statisticians. A step-by-step presentation of the material will be provided to ensure that students grasp the fundamental concepts and are able to then develop further theory and methodology at the end of the lectures.
Optimization: Theory and Algorithms
Robert Vanderbei, Princeton University
The course will cover linear, convex, and parametric optimization. In each of these areas, the role of duality will be emphasized as it informs the design of efficient algorithms and provides a rigorous basis for determining optimality. Various versions of the Simplex Method for linear programming will be presented. The dangers of degeneracy and ways to avoid it will be explained. Also, both the worst-case and average-case efficiency of the algorithms will be described. Finally, an efficient algorithm for parametrically solving multi-objective optimization problems will be presented, analyzed, and proposed as a new algorithm for sparse regression.
Bayesian Modelling
Zoubin Ghahramani, University of Cambridge
Graphical Models
Zoubin Ghahramani, University of Cambridge
Applications of Bayesian Modelling
Zoubin Ghahramani, University of Cambridge
Introduction to Bayesian Nonparametrics
Peter Orbanz, University of Cambridge
Advanced Bayesian Nonparametrics
Peter Orbanz, University of Cambridge
Gaussian Processes
John Cunningham, University of Cambridge
Dirichlet Process Practical
Dilan Görür, Yahoo! Labs
Gaussian Process Practical
Dilan Görür, Yahoo! Labs
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