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BayesMAP is an upcoming paper about techniques for estimating posterior modes using Proximal algorithms. The Proximal approach is shown to be a good alternative for Bayesian posterior estimation and has the potential to outperform standard methods in terms of speed and scalability. In regards to sparsity, we find that Proximal algorithms perform particularly well, can at times be easily accelerated, and provide exact solutions where some commonly-used approaches do not.
These examples are currently in development and ultimately for demonstration purposes only, and not intended for direct application. We’re building an R package (aptly named BayesMAP) comprised of refined versions of these algorithms combined into a single bayesmap(...) function with glm-like behavior.
This example site is also intended to be an open-source, collaborative endeavour, so, if anyone is interested in contributing, we’ll be posting a link to a Git repository shortly, but in the meantime use the contact link in the footer to get involved.
Here we estimate an \(L^2\) loss and \(\ell_1\) penalty model (also known as Lasso) using Proximal Gradient methods.
Here we estimate a Logit loss with double-Pareto penalty using Half Quadratic and Proximal methods.