A1035
Title: Proximal MCMC for Bayesian inference of constrained and regularized estimation
Authors: Eric Chi - Rice University (United States) [presenting]
Abstract: Proximal Markov Chain Monte Carlo (MCMC) is a flexible and general Bayesian inference framework for constrained or regularized parametric estimation. The basic idea of proximal MCMC is to approximate non-smooth regularization terms via the Moreau-Yosida envelope. Initial proximal MCMC strategies, however, fixed nuisance and regularization parameters as constants and relied on the Langevin algorithm for the posterior sampling. Proximal MCMC is extended to a fully Bayesian framework with modeling and data-adaptive estimation of all parameters, including regularization parameters. More efficient sampling algorithms, such as the Hamiltonian Monte Carlo, are employed to scale proximal MCMC to high-dimensional problems. The proposed proximal MCMC offers a versatile and modularized procedure for the inference of constrained and non-smooth problems that are mostly tuning parameter-free. Its utility is illustrated in various statistical estimation and machine-learning tasks.
