Scaling Up Bayesian Neural Networks with Neural Networks

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Statistics

Background:

• Bayesian Neural Networks (BNNs) provide robust uncertainty quantification in deep learning.
• Conventional BNNs face challenges with computational intensity (MCMC) or underestimating uncertainty (variational inference).
• Existing methods struggle with data requirements and overfitting common in deep learning.

Purpose of the Study:

• To develop a computationally efficient strategy for Bayesian Neural Networks.
• To improve the speed of uncertainty quantification in deep learning models.
• To address the limitations of existing MCMC and variational inference methods for BNNs.

Main Methods:

• Proposed a novel Calibration-Emulation-Sampling (CES) strategy for BNNs.
• Utilized a small set of parameter samples for initial calibration.
• Developed an emulator to approximate the posterior probability map for faster sampling.

Main Results:

• Demonstrated significant improvements in computational efficiency for BNNs.
• Maintained comparable prediction accuracy to standard BNN methods.
• Showcased effective uncertainty quantification capabilities with the CES strategy.
• Validated the approach using both simulated and real-world datasets.

Conclusions:

• The CES strategy offers a computationally efficient alternative for BNNs.
• This method enhances the practical applicability of BNNs in deep learning.
• CES successfully balances computational speed with accurate uncertainty estimation.