Efficient Variational Bayesian Approximation Method Based on Subspace optimization

Yuling Zheng (1) , Aurélia Fraysse (1) , Thomas Rodet (2)

1 L2S - Laboratoire des signaux et systèmes
2 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

Variational Bayesian approximations have been widely used in fully Bayesian inference for approx- imating an intractable posterior distribution by a separable one. Nevertheless, the classical variational Bayesian approximation (VBA) method suffers from slow convergence to the approximate solution when tackling large-dimensional problems. To address this problem, we propose in this paper an improved VBA method. Actually, variational Bayesian issue can be seen as a convex functional optimization problem. The proposed method is based on the adaptation of subspace optimization methods in Hilbert spaces to the function space involved, in order to solve this optimization problem in an iterative way. The aim is to determine an optimal direction at each iteration in order to get a more efficient method. We highlight the efficiency of our new VBA method and its application to image processing by considering an ill-posed linear inverse problem using a total variation prior. Comparisons with state of the art variational Bayesian methods through a numerical example show the notable improved computation time.

Domaines: Sciences de l'ingénieur [physics]; Mathématiques [math]

Yuling Zheng, Aurélia Fraysse, Thomas Rodet. Efficient Variational Bayesian Approximation Method Based on Subspace optimization. IEEE Transactions on Image Processing, 2015, 24 (2), pp.681-693. ⟨10.1109/TIP.2014.2383321⟩. ⟨hal-00990003⟩