Quantification of Uncertainties in Probabilistic Deep Neural Network by Implementing Boosting of Variational Inference

Abstract: Modern neural network architectures have achieved remarkable accuracies but remain highly dependent on their training data, often lacking interpretability in their learned mappings. While effective on large datasets, they tend to overfit on smaller ones. Probabilistic neural networks, such as those utilizing variational inference, address this limitation by incorporating uncertainty estimation through weight distributions rather than point estimates. However, standard variational inference often relies on a single-density approximation, which can lead to poor posterior estimates and hinder model performance. We propose Boosted Bayesian Neural Networks (BBNN), a novel approach that enhances neural network weight distribution approximations using Boosting Variational Inference (BVI). By iteratively constructing a mixture of densities, BVI expands the approximating family, enabling a more expressive posterior that leads to improved generalization and uncertainty estimation. While this approach increases computational complexity, it significantly enhances accuracy an essential tradeoff, particularly in high-stakes applications such as medical diagnostics, where false negatives can have severe consequences. Our experimental results demonstrate that BBNN achieves ~5% higher accuracy compared to conventional neural networks while providing superior uncertainty quantification. This improvement highlights the effectiveness of leveraging a mixture-based variational family to better approximate the posterior distribution, ultimately advancing probabilistic deep learning.