Proxgamma

Proxgamma is a term that sometimes appears in discussions related to Bayesian statistics and computational methods for approximating posterior distributions. It refers to a specific type of approximation algorithm. While not a universally standard or formal term with a single, widely accepted definition, it generally implies a proximal gradient-based approach used within a Monte Carlo or variational inference framework.

The core idea behind proximal methods is to efficiently handle objective functions that are sums of two parts: a smooth, differentiable part and a non-smooth, potentially non-differentiable part. Proximal gradient algorithms update parameters by taking a gradient step on the smooth part and then applying a "proximal operator" to the non-smooth part. This proximal operator effectively handles the non-smoothness, which might represent constraints, penalties, or other regularizing terms.

In the context of Bayesian inference, the posterior distribution is often the target of approximation. When this posterior or its log-density can be decomposed into smooth and non-smooth components, proximal methods can be adapted. For example, in variational inference, where the goal is to minimize a divergence (like the KL divergence) between an approximating distribution and the true posterior, proximal techniques might be employed to optimize the variational objective. Similarly, in certain Markov Chain Monte Carlo (MCMC) algorithms, proximal ideas could be incorporated to improve sampler efficiency, especially when dealing with models that have structured or non-smooth components in their probability distributions. The "proxgamma" moniker itself might originate from a specific software implementation or a research paper that coined the term to describe their particular proximal algorithm applied to a gamma distribution or a related problem.