BLASSO_SA

MAP estimation of the Bayesian LASSO via Simulated Annealing.

NOTE

Depends on a submodule (for sampling from the Generalized Inverse Gaussian), so don't forget to initialize and update the submodules when cloning the repo.

Sampler

The Simulated Annealing is based on the Gibbs sampler presented in [1] (with marginalized out μ).

Cooling down of the posterior conditionals can be achieved by a parameter shift of the distributions. For the Inverse Gaussian distribution we make use of the fact that we can represent an IG as a Generalized Inverse Gaussian with p=-0.5.

Let T be the current Temperature. Then we can sample according to:

Sampling from the Normal

We want to avoid having to directly invert A:

solve for b by backward subtitution and for μ by forward and backward substitution.

Example

Example Jupyter Notebook

References

[1] Park, Trevor, and George Casella. "The bayesian lasso." Journal of the American Statistical Association 103.482 (2008): 681-686.