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I am currently working on ridge regression, which can be interpreted using Bayesian statistics (DOI: 10.1016/j.electacta.2015.03.123). In particular, I know that the maximum-a-posteriori (MAP) estimate can be computed with its uncertainty.

However, is it possible to evaluate the MAP when the 1-norm is used instead of the 2-norm, i.e., for lasso regression? Moreover, how do you sample with the 1-norm?

kjetil b halvorsen
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  • You seem to be interested in bayesian lasso. Maybe a duplicate: https://stats.stackexchange.com/questions/108466/bayesian-lasso-vs-ordinary-lasso, https://stats.stackexchange.com/questions/368002/lasso-and-ridge-from-the-bayesian-perspective-what-about-the-tuning-parameter, https://stats.stackexchange.com/questions/560977/lasso-or-ridge-vs-bayesian-map, https://stats.stackexchange.com/questions/184590/bayesian-lasso-vs-spike-and-slab, https://stats.stackexchange.com/questions/551673/bayesian-elastic-lasso and search this site. – kjetil b halvorsen Mar 08 '24 at 22:06

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