[Gaussian Processes in Practice Logo] Gaussian Processes in Practice

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Workshop Schedule

09:00 - 09:30 Coach Pick up from Hilton, Campanile and Caldecott Arms. Be ready at 9:00.
09:30 - 09:45 Welcome
  Neil Lawrence
09:45 - 10:45 Gaussian Process Basics [slides]
  David MacKay, Department of Physics, University of Cambridge, U.K.
  "How on earth can a plain old Gaussian distribution be useful for sophisticated regression and machine learning tasks?"
10:45 - 11:15 Coffee Break
11:15 - 12:15 Interpreting Covariance Functions & Classification [slides]
  Carl Rasmussen, Max-Planck Institute, Tuebingen, Germany
12:15 - 12:35 Spotlights of Poster Presentations
  How to choose the covariance for Gaussian process regression independently of the basis
[slides]
Matthias O. Franz and Peter V. Gehler, MPI Tuebingen, Germany

An Exchanging-based Refinement to Sparse Gaussian Process Regression
[poster]
Ping Sun and Xin Yao, School of Computer Science, University of Birmingham, U.K.

Learning RoboCup-Keepaway with Kernels
[slides]
Tobias Jung and Daniel Polani, University of Mainz, Germany and University of Hertfordshire, U.K.

Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology
[slides]
Aki Vehtari and Jarno Vanhatalo, Helsinki University of Technology, Finland

12:35 - 13:30 Lunch Break
13:30 - 14:30 Eigenfunctions & Approximation Methods [slides]
  Chris Williams, School of Informatics, University of Edinburgh, U.K.
14:30 - 15:00 Flexible and efficient Gaussian process models [slides]
  Edward Snelson, Gatsby Computational Neuroscience Unit, University College London, U.K.
  I will briefly describe our work on the sparse pseudo-input Gaussian process (SPGP), where we refine the sparse approximation by selecting `pseudo-inputs' using gradient methods. I will then describe several extensions to this framework. Firstly we incorporate supervised dimensionality reduction to deal with high dimensional input spaces. Secondly we develop a version of the SPGP that can handle input-dependent noise. These extensions allow GP methods to be applied to a wider variety of modelling tasks than previously possible.

Joint work with Zoubin Ghahramani.

15:00 - 15:30 Analysing Gene Expression Data Using Gaussian Processes [slides]
  Lorenz Wernisch, School of Crystallography, Birkbeck College, U.K.
  Complex gene regulatory mechanisms ensure the proper functioning of biological cells. New high-throughput experimental techniques, such as microarrays, provide a snapshot of gene expression levels of thousands of genes at the same time. If repeated on a sample of synchronized cells, time-series profiles of gene activity can be obtained. The aim is to reconstruct the complex gene regulatory network underlying these profiles. Genes often influence each other in a nonlinear fashion and with intricate interaction patterns. Linear models are often unsuited to capture such relationships. Gaussian processes, on the other hand, are ideal for representing nonlinear relationships. A particular attraction is the automatic relevance determination effect, removing unused inputs and resulting in sparse gene networks.
15:30 - 16:00 Tea Break
16:00 - 16:30 Gaussian Process Model for Inferring the Regulatory Activity of Transcription Factor Proteins [slides]
  Guido Sanguinetti, Department of Computer Science, University of Sheffield, U.K.
  Inferring the concentration of transcription factors' proteins from the expression levels of target genes is a very active area of research in computational biology. Usually, the dynamics of the gene expression levels are modelled using differential equations where the transcription factor protein concentrations are treated as parameters, subsequently estimated using MCMC. We show how this inference problem can be solved more elegantly by placing a GP prior over the latent functions, obtaining comparable results to the standard MCMC approach in a fraction of the time.

Joint work with Neil Lawrence and Magnus Rattray.
16:30 - 16:45 Spotlights of Poster Presentations
  Gaussian Processes for Principal Component Analysis
[slides]
Colin Fyfe, University of Paisley, U.K.

Gaussian Processes for Prediction in Intensive Care
[slides]
Fabian Guiza, Jan Ramon and Hendrik Blockeel, Department of Computer Science, K. U. Leuven, Belgium

Gaussian Processes for Active Sensor Management
[slides]
Alexander N. Dolia, Chris Harris, John Shawe-Taylor, University of Southampton, U.K. and Tijl De Bie, OKP Research Group, K. U. Leuven, Belgium

16:45 - 17:15 Discussion Time [slides]
  Discussion Panel
17:30 - 19:00 Tour of Bletchley Park
19:30 - 21:30 Dinner
 
  • Goats Cheese with Cranberry Relish and Salad Garnish (v)
  • Braised Lamb Shank in a Red Wine, Garlic and Rosemary Sauce
  • Meringue Nets filled with Cream, Rasberries and Coulis
A vegetarian alternative to the main course will be provided to attendees who register as vegetarian.
21:30 - 21:45 Coach back to hotels.

Tuesday 13 June

09:00 - 09:30 Coach Pick up from Hilton, Campanile and Premier Travel Inn (Caldecott Arms). Be ready at 9:00.
09:30 - 10:30 Learning Human Pose and Motion Models for Animation [slides]
  Aaron Hertzmann, Department of Computer Science, University of Toronto, Canada
  Computer animation is an extraordinarily labor-intensive process; obtaining high-quality motion models could make the process faster and easier. I will describe methods for learning models of human poses and motion from motion capture data. I will begin with a pose model based on the Gaussian Process Latent Variable Model (GPLVM), and the application of this model to Inverse Kinematics posing. I will then describe the Gaussian Process Dynamical Model (GPDM) for modeling motion dynamics. I may also mention a few other extensions to the GPLVM for modeling motion data. I will discuss the properties of these models (both good and bad) and potential directions for future work.

Joint work with David Fleet, Keith Grochow, Steven L. Martin, Zoran Popovic, Jack Wang
10:30 - 11:00 Gaussian Processes for Monocular 3D People tracking [slides]
  Raquel Urtasun, Computer Vision Laboratory, EPFL, Switzerland
  We advocate the use of Gaussian Processes (GPs) to learn prior models of human pose and motion for 3D people tracking. The Gaussian Process Latent variable model (GPLVM) provides a low-dimensional embedding of the human pose, and defines a density function that gives higher probability to poses close to the training data. The Gaussian Process Dynamical Model (GPDM) provides also a complex dynamical model in terms of another GP. With the use of Bayesian model averaging both GPLVM and GPDM can be learned from relatively small amounts of training data, and they generalize gracefully to motions outside the training set. We show that such priors are effective for tracking a range of human walking styles, despite weak and noisy image measurements and a very simple image likelihood. Tracking is formulated in terms of a MAP estimator on short sequences of poses within a sliding temporal window.

Joint work with Jack Wang, David Fleet, Aaron Hertzmann and Pascal Fua
11:00 - 11:30 Coffee Break
11:30 - 12:00 Gaussian Process Implicit Surfaces [slides]
  Oliver Williams, Microsoft Research, Cambridge, U.K.
  Many applications in computer vision and computer graphics require the definition of curves and surfaces. Implicit surfaces are a popular choice for this because they are smooth, can be appropriately constrained by known geometry, and require no special treatment for topology changes. In this paper we use Gaussian processes for this and derive a covariance function equivalent to the thin plate spline regularizer which has desirable properties for shape modelling. We demonstrate our approach for both 2D curves and 3D surfaces. The benefit of using a Gaussian process for this is the meaningful probabilistic representation of the function.

Joint work with Andrew Fitzgibbon.
12:00 - 12:30 Minimum Likelihood Image Feature and Scale Detection Based on the Brownian Image Model [slides]
  Kim S. Pedersen, The Image Group, IT University of Copenhagen, Denmark
  We present a novel approach to image feature and scale detection based on the fractional Brownian image model in which images are realisations of a Gaussian random process on the plane. Image features are points of interest usually sparsely distributed in images. We propose to detect such points and their intrinsic scale by detecting points in scale-space that locally minimises the likelihood under the model.

Joint work with Peter van Dorst and Marco Loog.

12:30 - 13:30 Lunch Break
13:30 - 14:00 Demonstration of the Colossus Mark II Computer
  Tony Sale, Bletchley Park
14:00 - 14:30 Wifi Localization with Gaussian Processes [slides]
  Brian Ferris, Department of Computer Science and Engineering, University of Washington, U.S.A.
  Estimating the location of a mobile device from wireless signal strength is an interesting research problem, especially given the complexity of signal propagation through space in the presence of obstacles such as buildings, walls, or people. Gaussian processes have already been used to solve such signal strength localization problems. We extend this work to indoor WiFi localization and present novel kernel functions which increase the accuracy of the Gaussian process model, especially when faced with sparse training data. We additionally present preliminary results of simultaneous mapping and localization using Gaussian process latent variable modeling.

Joint work with Dieter Fox.
14:30 - 15:00 Learning to Control an Octopus Arm with Gaussian Process Temporal Difference Methods [slides]
  Yaakov Engel, Department of Computing Science, University of Alberta, Canada
  The Octopus arm is a highly versatile and complex limb. How the Octopus controls such a hyper-redundant arm (not to mention eight of them!) is as yet unknown. Robotic arms based on the same mechanical principles may render present day robotic arms obsolete. In this talk, I will describe how we tackle this problem using an online reinforcement learning algorithm, based on a Bayesian approach to policy evaluation known as Gaussian process temporal difference (GPTD) learning.

Our substitute for the real arm is a computer simulation of a 2-dimensional model of an Octopus arm. Even with the simplifications inherent to this model, the state space we face is a high-dimensional one, for any arm of reasonable size. We apply a GPTD-based algorithm to this domain, and demonstrate its operation on several learning tasks of varying degrees of difficulty.

Joint work with Peter Szabo and Dmitry Volkinshtein.

15:00 - 15:30 Gaussian Process Approximations of Stochastic Differential Equations [slides]
  Cedric Archambeau, School of Electronics and Computer Science, University of Southampton, U.K.
  It is well known that certain classes of Gaussian process arise naturally as solutions to stochastic differential equations, for example the Ornstein-Uhlenbeck process arises as the stationary solution of a simple linear stochastic differential equation. In this work we introduce some initial results on the approximation of the solution of general stochastic differential equations by Gaussian processes. We employ a variational framework, where we seek a Gaussian process approximation to the posterior distribution of the state of a system whose dynamics are governed by a stochastic differential equation. The application for this work is approximate inference within stochastic dynamic models, in particular models used in weather forecasting.

Joint work with Dan Cornford, Manfred Opper and John Shawe-Taylor
15:30 - 16:00 Tea Break
16:00 - 17:00 Discussion Time [slides]
  Discussion Panel
17:30 - 17:45 Coach back to hotels and to Milton Keynes and Bletchley Railway Stations.