Host Institution: 
University of Newcastle 
Title of Seminar: 
SigmaOpt talk: A finite element method for density estimation with Gaussian process priors 
Speaker's Name: 
Professor Markus Hegland 
Speaker's Institution: 
Australian National University 
Time and Date: 
Monday 21st November, 2011, 2:30 PM (AEDT) 
Seminar Abstract: 
Probability densities are a major tool in exploratory statistics and stochastic modelling. I will talk about a numerical technique for the estimation of a probability distribution from scattered data using exponential families and a maximum aposteriori approach with Gaussian process priors. Using CameronMartin theory, it can be seen that density estimation leads to a nonlinear variational problem with a functional defined on a reproducing kernel Hilbert space. This functional is strictly convex. A dual problem based on Fenchel duality will also be given. The (original) problem is solved using a NewtonGalerkin method with damping for global convergence. In this talk I will discuss some theoretical results relating to the numerical solution of the variational problem and the results of some computational experiments. A major challenge is of course the curse of dimensionality which appears when highdimensional probability distributions are estimated. 
Seminar Convenor: 
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AGR IT support: 
