Variational learning and bits-back coding: an information-theoretic view to Bayesian learning

Area of Science:

• Machine Learning
• Information Theory
• Computational Neuroscience

Background:

• Bits-back coding, introduced by Wallace (1990) and Hinton & van Camp (1993), connects Bayesian learning with minimum description length (MDL) principles.
• Variational Bayesian methods, particularly ensemble learning, utilize cost functions that can be interpreted through the lens of information theory.
• Understanding the relationship between Bayesian inference and information-theoretic approaches is crucial for advancing machine learning models.

Purpose of the Study:

• To demonstrate the benefits of integrating Bayesian and information-theoretic viewpoints using bits-back coding.
• To interpret the cost function in variational Bayesian ensemble learning as a code length.
• To provide novel insights into the learning process and model components in hierarchical latent variable models.

Main Methods:

• Utilizing bits-back coding to link Bayesian and MDL learning frameworks.
• Applying variational Bayesian inference to hierarchical latent variable models.
• Analyzing the cost function as a code length to understand posterior approximation misfit and model evidence bounds.

Main Results:

• The bits-back coding framework provides a dual interpretation: Bayesian misfit and information-theoretic code length.
• This dual view offers valuable insights into model comparison, pruning, and other aspects of the learning process.
• The approach elucidates phenomena observed during the learning of hierarchical latent variable models.

Conclusions:

• The integration of Bayesian and MDL perspectives via bits-back coding enhances the understanding of learning mechanisms.
• This unified view is particularly beneficial for analyzing and optimizing hierarchical latent variable models.
• The code-length interpretation offers a powerful tool for model selection and understanding model complexity in machine learning.