Flexible Bayesian Last Layer Models Using Implicit Priors and Diffusion Posterior Sampling

TL;DR

This paper introduces a novel Bayesian last layer modeling approach that uses implicit priors and diffusion sampling to improve expressiveness, accuracy, and uncertainty quantification in neural networks, especially on complex datasets.

Contribution

It proposes combining diffusion techniques with implicit priors for variational learning in Bayesian last layer models, enhancing their flexibility and performance.

Findings

Improved predictive accuracy on complex datasets.

Enhanced uncertainty calibration and out-of-distribution detection.

Maintained computational efficiency with explicit variational bounds.

Abstract

Bayesian Last Layer (BLL) models focus solely on uncertainty in the output layer of neural networks, demonstrating comparable performance to more complex Bayesian models. However, the use of Gaussian priors for last layer weights in Bayesian Last Layer (BLL) models limits their expressive capacity when faced with non-Gaussian, outlier-rich, or high-dimensional datasets. To address this shortfall, we introduce a novel approach that combines diffusion techniques and implicit priors for variational learning of Bayesian last layer weights. This method leverages implicit distributions for modeling weight priors in BLL, coupled with diffusion samplers for approximating true posterior predictions, thereby establishing a comprehensive Bayesian prior and posterior estimation strategy. By delivering an explicit and computationally efficient variational lower bound, our method aims to augment the expressive abilities of BLL models, enhancing model accuracy, calibration, and out-of-distribution detection proficiency. Through detailed exploration and experimental validation, We showcase the method's potential for improving predictive accuracy and uncertainty quantification while ensuring computational efficiency.