Variationally Inferred Sampling through a Refined Bound.

Area of Science:

• Machine Learning
• Computational Statistics

Background:

• Bayesian inference is crucial for probabilistic models but computationally intensive.
• Variational methods offer approximations but can lack accuracy.
• Markov chain samplers are accurate but can be slow to converge.

Purpose of the Study:

• To develop a computationally efficient framework for Bayesian inference.
• To improve the speed and accuracy of probabilistic model analysis.
• To introduce a novel method combining variational approximations and Markov chain sampling.

Main Methods:

• Embedding a Markov chain sampler within a variational posterior approximation framework.
• Developing strategies for approximating evidence lower bound (ELBO) computation.
• Utilizing automatic differentiation for automatic tuning of sampler parameters and faster mixing times.

Main Results:

• Demonstrated significant efficiency gains in Bayesian inference.
• Achieved faster mixing times through automatic parameter tuning.
• Showcased effective performance on diverse applications including time-series analysis, density estimation, and classification.

Conclusions:

• The refined variational approximation framework offers a powerful and efficient approach to Bayesian inference.
• The method is versatile, applicable to various probabilistic models and data types.
• Ease of implementation and automatic tuning make it a practical tool for researchers.