Plug-and-Play Split Gibbs Sampler: Embedding Deep Generative Priors in Bayesian Inference.

Area of Science:

• Computational statistics
• Machine learning
• Image processing

Background:

• Posterior distribution sampling is crucial in Bayesian inference but computationally challenging.
• Existing plug-and-play (PnP) methods often yield point estimates and require explicit priors.
• Deep generative models offer powerful prior representations but integrating them into sampling remains an active research area.

Purpose of the Study:

• To introduce a novel stochastic plug-and-play (PnP) sampling algorithm for efficient posterior distribution sampling.
• To leverage variable splitting and deep generative models for Bayesian denoising tasks.
• To enable Bayesian estimators to provide confidence intervals, enhancing uncertainty quantification.

Main Methods:

• Developed a stochastic PnP algorithm based on split Gibbs sampling (SGS).
• Inspired by half-quadratic splitting (HQS) and alternating direction method of multipliers (ADMM).
• Integrated state-of-the-art diffusion-based generative models for the Bayesian denoising subproblem.

Main Results:

• The proposed SGS algorithm efficiently samples from posterior distributions.
• The method implicitly encodes prior information within pre-trained generative models, avoiding explicit prior selection.
• Unlike deterministic PnP methods, the stochastic approach provides confidence intervals with minimal extra computational cost.

Conclusions:

• The stochastic PnP sampling strategy is efficient for image processing tasks.
• The algorithm offers a principled way to incorporate deep generative models into Bayesian inference.
• This approach enhances uncertainty quantification in Bayesian estimation by providing confidence intervals.