It's similar to lasso where the Laplace distribution is decomposed using a gaussian mixture scaled with an exponential/gamma distribution. In group lasso, there

It's similar to lasso where the Laplace distribution is decomposed using a gaussian mixture scaled with an exponential/gamma distribution. In group lasso, there is one variance term per group which is generated by the exponential/gamma prior. See https://www.cs.ubc.ca/~murphyk/MLbook/ https://www.cs.ubc.ca/~murphyk/MLbook/ for the mathematical decomp. It should be noted that obtained using that prior in a MAP estimation per the other comment.