| EPSRC Reference: |
GR/M56005/01 |
| Title: |
THE GEOMETRY OF PARAMETER SPACES FOR LEARNING ON BAYESIAN NETWORKS |
| Principal Investigator: |
Smith, Professor JQ |
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| Department: |
Statistics |
| Organisation: |
University of Warwick |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 September 1999 |
Ends: |
31 August 2002 |
Value (£): |
127,881
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| EPSRC Research Topic Classifications: |
| Statistics & Appl. Probability |
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| EPSRC Industrial Sector Classifications: |
| Manufacturing |
Chemicals |
| Pharmaceuticals and Biotechnology |
Energy |
| Information Technologies |
No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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This research will investigate the geometry of parameter spaces which describe Bayesian networks when information about some of their variables is systematically missing. Although such graphical models with hidden variables are pervasive in applications, including for example all Bayesian neural networks, they are known often to exhibit unpleasant properties such as lack of identifiability and non-convergence of numerical algorithms. Recent results have shown that graphical models, which are characterised by a set of conditional independence statements, equivalently demand set of algebraic equations to be satisfied over the parameter space of the system when all variables are discrete. In this project real algebraic geometrical techniques will be exploited to characterise and explain the singularities behind the typical unidentifiability of these models. This framework will enable us to discover both which aspects of the specification of the prior distribution will be enduring and also how the model or numerical algorithms can be adapted to ensure good convergence characteristics. We shall also develop more efficient model diagnostics and selection statistics on the basis of insight given by this geometry to help detect from the data whether a given Bayesian network is appropriate and if not, how it should be modified so that it is.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.warwick.ac.uk |