Bayesian Neural Networks vs. Mixture Density Networks: Theoretical and Empirical Insights for Uncertainty-Aware Nonlinear Modeling
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909875473219584 |
|---|---|
| author | Ghosh, Riddhi Pratim Barnett, Ian |
| author_facet | Ghosh, Riddhi Pratim Barnett, Ian |
| contents | This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by placing prior distributions over network parameters, MDNs directly model the conditional output distribution, thereby capturing multimodal and heteroscedastic data-generating mechanisms. We present a unified theoretical and empirical framework comparing these approaches. On the theoretical side, we derive convergence rates and error bounds under Hölder smoothness conditions, showing that MDNs achieve faster Kullback-Leibler (KL) divergence convergence due to their likelihood-based nature, whereas BNNs exhibit additional approximation bias induced by variational inference. Empirically, we evaluate both architectures on synthetic nonlinear datasets and a radiographic benchmark (RSNA Pediatric Bone Age Challenge). Quantitative and qualitative results demonstrate that MDNs more effectively capture multimodal responses and adaptive uncertainty, whereas BNNs provide more interpretable epistemic uncertainty under limited data. Our findings clarify the complementary strengths of posterior-based and likelihood-based probabilistic learning, offering guidance for uncertainty-aware modeling in nonlinear systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Neural Networks vs. Mixture Density Networks: Theoretical and Empirical Insights for Uncertainty-Aware Nonlinear Modeling Ghosh, Riddhi Pratim Barnett, Ian Computation Machine Learning 68T07, 62G08, 62C10, 41A25 This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by placing prior distributions over network parameters, MDNs directly model the conditional output distribution, thereby capturing multimodal and heteroscedastic data-generating mechanisms. We present a unified theoretical and empirical framework comparing these approaches. On the theoretical side, we derive convergence rates and error bounds under Hölder smoothness conditions, showing that MDNs achieve faster Kullback-Leibler (KL) divergence convergence due to their likelihood-based nature, whereas BNNs exhibit additional approximation bias induced by variational inference. Empirically, we evaluate both architectures on synthetic nonlinear datasets and a radiographic benchmark (RSNA Pediatric Bone Age Challenge). Quantitative and qualitative results demonstrate that MDNs more effectively capture multimodal responses and adaptive uncertainty, whereas BNNs provide more interpretable epistemic uncertainty under limited data. Our findings clarify the complementary strengths of posterior-based and likelihood-based probabilistic learning, offering guidance for uncertainty-aware modeling in nonlinear systems. |
| title | Bayesian Neural Networks vs. Mixture Density Networks: Theoretical and Empirical Insights for Uncertainty-Aware Nonlinear Modeling |
| topic | Computation Machine Learning 68T07, 62G08, 62C10, 41A25 |
| url | https://arxiv.org/abs/2510.25001 |