Sparse Bayesian inference with regularized Gaussian distributions

Music City Center 

In this talk, we will present a family of sparsity promoting Bayesian hierarchical models based on combining Gaussian distributions with the deterministic effects of sparsity-promoting regularization like $l_1$ norms, total variation and/or constraints. Unlike Bayesian hierarchical models based on conditional continuous distributions, for example, conditional Gaussian distributions, using regularized Gaussian distributions results in sparse samples without needing large hierarchical models. We will show how to derive approximate Gibbs samplers for these hierarchical models and discuss advantages and disadvantages of the presented method with regard to theory, modeling and computation.

Bayesian inverse problems

sparsity