Sampling the Variational Posterior with Local Refinement.

Area of Science:

• Machine Learning
• Computational Statistics
• Bayesian Inference

Background:

• Variational inference approximates posterior distributions in Bayesian models.
• A challenge is balancing computational tractability with posterior expressiveness.
• Existing methods may struggle with complex posterior dependencies and multi-modality.

Purpose of the Study:

• To propose a novel variational inference method for generating flexible posterior approximations.
• To enable the capture of posterior dependencies and multi-modality.
• To improve the quality of variational approximations in Bayesian probabilistic models.

Main Methods:

• A novel sampling method that refines a coarse initial approximation in local regions.
• Theoretical demonstration of improved approximation quality using the evidence lower bound (ELBO).
• Experimental validation on hierarchical models, deep neural networks, and contextual bandit problems.

Main Results:

• The proposed method consistently improves approximation quality.
• Outperforms recent variational inference methods in terms of log-likelihood and ELBO.
• Successfully captures posterior dependencies and multi-modality absent in initial approximations.

Conclusions:

• The novel local refinement method offers a more flexible and accurate approach to variational inference.
• This technique enhances Bayesian inference for complex models and large datasets.
• The method demonstrates superior performance across diverse machine learning tasks.