Understanding the Trade-offs in Accuracy and Uncertainty Quantification: Architecture and Inference Choices in Bayesian Neural Networks (2503.11808v2)

Abstract: As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior predictive distribution of Bayesian neural networks, the properties of even the most commonly used posterior approximations are often questioned. Computational burdens and intractable posteriors expose miscalibrated Bayesian neural networks to poor accuracy and unreliable uncertainty estimates. Approximate Bayesian inference aims to replace unknown and intractable posterior distributions with some simpler but feasible distributions. The dimensions of modern deep models, coupled with the lack of identifiability, make Markov chain Monte Carlo (MCMC) tremendously expensive and unable to fully explore the multimodal posterior. On the other hand, variational inference benefits from improved computational complexity but lacks the asymptotical guarantees of sampling-based inference and tends to concentrate around a single mode. The performance of both approaches heavily depends on architectural choices; this paper aims to shed some light on this by considering the computational costs, accuracy and uncertainty quantification in different scenarios including large width and out-of-sample data. To improve posterior exploration, different model averaging and ensembling techniques are studied, along with their benefits on predictive performance. In our experiments, variational inference overall provided better uncertainty quantification than MCMC; further, stacking and ensembles of variational approximations provided comparable accuracy to MCMC at a much-reduced cost.

• The paper analyzes the trade-offs between accuracy and uncertainty quantification in Bayesian Neural Networks by examining the interplay of network architecture and inference methods like MCMC and Variational Inference (VI).
• Empirical results show that VI, particularly with ReLU activation, can achieve comparable accuracy and better out-of-distribution uncertainty quantification than MCMC, although mean-field VI can face challenges.
• Practical implications suggest VI with ReLU offers a good balance for deployment, while future work should explore advanced VI techniques and improved model combination strategies like stacking and ensembles for enhanced performance.

Analyzing Architectural and Inference Choices in Bayesian Neural Networks

The paper "The Architecture and Evaluation of Bayesian Neural Networks" examines the intricacies of Bayesian Neural Networks (BNNs) and the impact of architectural selections in concert with inference techniques on both computational efficiency and prediction reliability. This analysis is contextualized in the framework of approximate Bayesian inference, specifically comparing Markov Chain Monte Carlo (MCMC) with Variational Inference (VI).

Overview of Bayesian Neural Networks

BNNs extend classical neural networks by incorporating probabilistic inference, offering the potential for enhanced uncertainty quantification. However, efficiently inferring the posterior distribution within BNNs presents significant computational challenges due to their complexity and high dimensionality. This paper contrasts two main approximate inference methods—MCMC, known for its theoretical robustness, but often computationally prohibitive, with VI, which offers computational efficiency but at the expense of approximate solutions lacking asymptotic guarantees.

Key Experiments and Findings

The paper presents a detailed empirical analysis involving:

1. Limited Width and Depth: The experiments investigate how BNN performance varies with network width (number of units) and depth (number of layers). Importantly, it was found that VI with rectified linear unit (ReLU) activation provides stable results but the mean-field Gaussian approximation—common in VI—can lead to degenerate solutions, especially with sigmoid activation in wide networks.
2. Out-of-Distribution (OOD) Robustness: The capability of BNNs to generalize and maintain reliable uncertainty estimates under OOD data is critical for applications in safety-sensitive fields. The paper shows that in these settings, VI approaches with ReLU activation not only achieve comparable accuracy to MCMC methods but also better uncertainty quantification.
3. Comparative Model Assessment: Employing tools such as the expected log pointwise predictive density (ELPD) via PSIS-LOO cross-validation provides effective measures for assessing model performance, especially in scenarios where test data distributions deviate from training sets.
4. Model Averaging and Stacking: The research extends into exploring model combination strategies like deep ensembles, stacking, and pseudo-Bayesian Model Averaging (pseudo-BMA). The findings suggest stacking and ensemble methods are beneficial for capturing the diversity of posterior predictions, thereby significantly enhancing predictive performance and uncertainty management compared to pseudo-BMA, notably in open-world scenarios where model completeness cannot be assumed.

Practical and Theoretical Implications

From a practical standpoint, the paper suggests that while MCMC could serve as a benchmark, its resource demand limits its practicality for complex networks. VI, particularly with ReLU activations, emerges as a balanced approach, merging feasible computational demands with satisfactory accuracy and uncertainty metrics, especially under increased network depth or width.

The theoretical implications encourage further exploration into developing more flexible VI families beyond mean-field and exploring alternative priors that could potentially address over-parameterization issues and enhance the calibration of uncertainty estimates.

Future Directions

The paper invites future exploration into several promising areas:

• Advanced VI Techniques: Exploring structured variational families and non-factorized approximations could address the under-explored complexity in the posterior landscape of BNNs.
• Sparsity-Inducing Priors: Approaches like shrinkage priors may help prevent overfitting in high-dimensional models while boosting computational efficiency.
• Improved Model Combinations: Innovations in stacking and ensembling, including node-wise integration and adaptive Bayesian approaches, could provide nuanced solutions to the multimodal challenges in BNN posteriors.

In conclusion, this paper provides significant insights into BNN design and inference, establishing directions for optimizing both predictive and computational performance through strategic architecture and method choices. The comparisons between inference strategies and architectural designs illuminate the nuanced trade-offs in BNN deployment, emphasizing the potential of VI under certain configurations as a scalable and robust alternative within Bayesian deep learning.