糖心TV

(Or: sample-based inference in large-scale inverse problems using

algorithms developed for computational optimization)

By Colin Fox

Abstract:

The Metropolis (Hastings-Green) algorithm for MCMC was invented in the

1950’s and has changed little since. In contrast, algorithms for

optimization that were also invented in the 1950’s have seen dramatic

improvement. We look to steal the developments in computational

optimization and apply them to sampling of probability distributions.

The connection between sampling and optimization is already close. For

example, Gibbs sampling of Gaussian distributions is exactly Gauss-Seidel

solution of linear equations – the iteration operators are identical and

convergence factors are identical. Polynomial acceleration developed for

iterative solvers can also accelerate Gibbs sampling giving optimal

convergence.

I will show some applications in large-scale inverse problems that

motivated this (ongoing) work, including sample-based inference in image

deblurring with non-negativity constraints computed using a sampling

version of the gradient-projected conjugate gradient algorithm.

organised by Andrew Stuart

LUNCH TO BE SERVED IN COMPLEXITY's COMMON ROOM