From a Bayesian perspective, it’s not entirely accurate to say that there is the same relationship between ridge/Gaussian-prior and lasso/Laplacian-prior. In th

From a Bayesian perspective, it’s not entirely accurate to say that there is the same relationship between ridge/Gaussian-prior and lasso/Laplacian-prior. In the first case, ridge regression yields a "proper" Bayesian estimator (e.g., mean of the posterior); the latter is only the MAP estimator, which is not really recommended from a purely Bayesian perspective. Ridge is also a MAP estimator, but that’s in addition to the stronger condition of minimizing the Bayes risk. There is a way to compute a "true" Bayesian Lasso, but it doesn’t yield a sparse model [0]. [0] http://archived.stat.ufl.edu/casella/Papers/Lasso.pdf http://archived.stat.ufl.edu/casella/Papers/Lasso.pdf