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Details of Grant 

EPSRC Reference: GR/M56005/01
Title: THE GEOMETRY OF PARAMETER SPACES FOR LEARNING ON BAYESIAN NETWORKS
Principal Investigator: Smith, Professor JQ
Other Investigators:
Mond, Professor D
Researcher Co-Investigators:
Project Partners:
Department: Statistics
Organisation: University of Warwick
Scheme: Standard Research (Pre-FEC)
Starts: 01 September 1999 Ends: 31 August 2002 Value (£): 127,881
EPSRC Research Topic Classifications:
Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
Manufacturing Pharmaceuticals and Biotechnology
Information Technologies No relevance to Underpinning Sectors
Energy Chemicals
Related Grants:
Panel History:  
Summary on Grant Application Form
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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Organisation Website: http://www.warwick.ac.uk