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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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