We are advertising a Microsoft Research funded PhD studentship in Machine Learning, on the subject of Learning and Inference in Highly Structured Continuous-Time Stochastic Systems. This Microsoft Research funded studentship is involved with the theoretical development and practical application of sequential Monte-Carlo methods (otherwise known as particle filters) for continuous time stochastic systems.
Many real-world systems are described by continuous differential equations through time in which some of the inputs are uncertain and hence can be described by probability distributions. Examples include weather forecasting, financial modelling, interaction models in systems biology and network traffic analysis. If the distributions are known, then there exist techniques for integrating the equations forward through time and hence evaluating (a probability distribution over) future predictions. A more challenging problem, but one of huge practical importance, is to reverse this process and to infer the nature of the unknown probability distributions over the inputs given a set of observed time sequences. In the simplest cases, the distributions have known parametric forms and we wish to infer the values of the parameters. Often, however, the form of the distributions themselves must also be inferred. More generally still, the structure of the equations (for example, the presence or absence of particular interactions) is also unknown, and again we would like to infer such structure from observations. Techniques for tackling such inference problems in the context of temporal systems are still in their infancy. The machine learning community has made significant advances in recent years in the solution of inference problems for static systems. This PhD studentship will involve collaborative research between Edinburgh University and Microsoft Research Cambridge, and aims to bring these techniques from machine learning to bear on the inference problem for continuous time stochastic systems. There may be possibility of an internship at Microsoft Research as part of the PhD.
In general, being able to harness inference and learning methods for continuous-time stochastic systems reaps benefits in situations where:
This PhD position would suit someone with a first degree in a mathematical or scientific discipline with high mathematical content. Ideally, the student would also have further study or experience of probabilistic machine learning or Bayesian statistics. Alternatively it may suit someone with a first degree in a computational discipline with high mathematical content, and who had studied probabilistic machine learning methods.
Informal enquiries regarding this studentship can be made to Dr Amos Storkey (a.storkey@ed.ac.uk). In order to apply, you should apply for a PhD to University of Edinburgh in the usual way, but specify that you are applying to Informatics, and would like to be considered for this studentship. You should include a statement of research interests, and details regarding what particular research direction you would be interested in within the remit of this post.
Applications should be made before March 31, 2008, although earlier application is preferable. Applications after that date may also be considered if the studentship has not already been filled.
The studentship is open to all applicants, both from the EU and from outside the EU. Further details can be found on the Microsoft Research PhD Scholarship pages.
To apply please submit an application form and the required application papers, including a statement of research interests (which should include details regarding the particular research direction you would be interested in within the remit of this studentship). Please state clearly, at question 21 on the application form, that you are applying for the Miscrosoft Studentship with Dr Amos Storkey.
This PhD post will be supervised by Amos Storkey, Chris Williams and Chris Bishop. Information on other PhD opportunities can be found at Amos Storkey: Jobs PhD Opportunities, and Chris Williams: Information for Prospective Students.