Deep bootstrap for Bayesian inference.

Area of Science:

• Statistics
• Machine Learning
• Computational Statistics

Background:

• Defining likelihoods is a core challenge in Bayesian inference.
• Traditional methods like Gibbs sampling and MCMC can be computationally intensive.
• Alternative approaches are needed for complex models where parameters are linked to data via loss functions.

Purpose of the Study:

• To explore Bayesian inference when parameters are linked to data through a loss function.
• To investigate novel computational approaches for approximating loss-driven posteriors.
• To introduce and evaluate deep bootstrap samplers for efficient Bayesian computation.

Main Methods:

• Surveyed existing Bayesian parametric and non-parametric inference methods.
• Focused on implicit bootstrap distributions defined via push-forward mappings.
• Developed and analyzed independent, identically distributed (iid) samplers using trained generative networks (deep bootstrap).
• Compared deep bootstrap samplers with exact bootstrap and Markov Chain Monte Carlo (MCMC).

Main Results:

• Deep bootstrap samplers achieve negligible simulation cost after training.
• These novel samplers demonstrate competitive performance against exact bootstrap and MCMC.
• Theoretical insights into bootstrap posteriors were provided through connections to model mis-specification.

Conclusions:

• Deep bootstrap methods offer a computationally efficient alternative for Bayesian inference in loss-driven models.
• These methods are particularly promising for complex statistical and machine learning applications.
• The study advances the prospects of Bayesian inference by providing new computational tools.