- SIGMAOPT SEMINAR
- Speaker: Markus Hegland, Mathematical Sciences Institute, Australian National University
- Title: A finite element method for density estimation with Gaussian process priors
- Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
- Access Grid Venue: UNewcastle [ENQUIRIES]
- Time and Date: 2:30 pm, Mon, 21st Nov 2011
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 a-posteriori approach with Gaussian process priors.
Using Cameron-Martin 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 Newton-Galerkin 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 high-dimensional probability distributions are estimated.
- Download: Talk slides (452 KB)
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