论文标题
受约束和正则化估计的贝叶斯推断的近端MCMC
Proximal MCMC for Bayesian Inference of Constrained and Regularized Estimation
论文作者
论文摘要
本文提倡马尔可夫链蒙特卡洛（Proxmcmc）作为柔性且普遍的贝叶斯推理框架，用于受约束或正则化估计。 ProxmCMC最初是在贝叶斯成像文献中引入的，它采用莫罗 - 耶西达包膜来平滑近似总差异正则化项，将方差和正则化强度参数作为常数，并使用langevin算法进行后取样。我们通过提供包括正则化强度参数在内的所有参数的数据自适应估计来扩展到完全贝叶斯。更强大的采样算法（例如哈密顿蒙特卡洛）被用来扩展固定问题到高维问题。与优化的近端算法相似，ProxMCMC提供了一种多功能和模块化的程序，用于对受约束和正常问题进行统计推断。在各种统计估计和机器学习任务上说明了ProxMCMC的力量，从常见主义者和贝叶斯的角度来看，这些统计估计和机器学习任务传统上都被认为是困难的。
This paper advocates proximal Markov Chain Monte Carlo (ProxMCMC) as a flexible and general Bayesian inference framework for constrained or regularized estimation. Originally introduced in the Bayesian imaging literature, ProxMCMC employs the Moreau-Yosida envelope for a smooth approximation of the total-variation regularization term, fixes variance and regularization strength parameters as constants, and uses the Langevin algorithm for the posterior sampling. We extend ProxMCMC to be fully Bayesian by providing data-adaptive estimation of all parameters including the regularization strength parameter. More powerful sampling algorithms such as Hamiltonian Monte Carlo are employed to scale ProxMCMC to high-dimensional problems. Analogous to the proximal algorithms in optimization, ProxMCMC offers a versatile and modularized procedure for conducting statistical inference on constrained and regularized problems. The power of ProxMCMC is illustrated on various statistical estimation and machine learning tasks, the inference of which is traditionally considered difficult from both frequentist and Bayesian perspectives.
