A measure-theoretic variational Bayesian algorithm for large dimensional problems

Abstract : In this paper we provide an algorithm allowing to solve the variational Bayesian issue as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of probability densities involved in the Bayesian methodology. The main advantage of this methodology is that it allows to address large dimensional inverse problems by unsupervised algorithms. The interest of our algorithm is enhanced by its application to large dimensional linear inverse problems involving sparse objects. Finally,we provide simulation results. First we show the good numerical performances of our method by comparing it with classical ones on a small tomographic problem. On a second time we treat a large dimensional dictionary learning problem and compare our method with a wavelet based one.
Complete list of metadatas

Cited literature [45 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00702259
Contributor : Aurélia Fraysse <>
Submitted on : Thursday, April 24, 2014 - 11:53:44 AM
Last modification on : Friday, April 19, 2019 - 1:28:12 PM
Long-term archiving on : Thursday, July 24, 2014 - 10:46:29 AM

File

var_bayHAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00702259, version 2

Citation

Aurélia Fraysse, Thomas Rodet. A measure-theoretic variational Bayesian algorithm for large dimensional problems. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2014, 7 (4), pp.2591-2622. ⟨hal-00702259v2⟩

Share

Metrics

Record views

585

Files downloads

326