Presented by: Mingyuan Zhou Duke University, ECE Feb 22, 2013

1. Large Scale Variational Bayesian Inference forStructured Scale Mixture ModelsYoung Jun Ko and Matthias SeegerICML 2012 Presented by: Mingyuan Zhou Duke University, ECE Feb 22, 2013

2. Introduction • Natural image statistics exhibit hierarchical dependencies across multiple scales. • Non-factorial latent tree models. • A large scale approximate Bayesian inference algorithm for linear models with non-factorial (latent tree-structured) scale mixture priors. • Experimental results on a range of denoising and inpainting problems demonstrate substantially improved performance compared to MAP estimation or to inference with factorial priors.

3. Structured Image Model • Impose sparsity

4. Structured Image Model • Non-factorial scale mixture model: • Output:

5. Example

7. Large Scale Variational Inference • Due to strong dependencies between components of u and s, factorial assumption might be restrictive. • Iterative decoupling • Decouple • Decouple mean and covariance components of • Prior:

8. Large Scale Variational Inference • VB

9. Large Scale Variational Inference

10. Image denoising

11. Image inpainting

14. Conclusions