Last Question
**We report here too our answer to Reviewer sJhN's last question**
*Are there any analyses of Computational Complexity that are specific to the use of credal sets as an approach to infer models? Can such an approach be implemented for limited but large datasets?*
We thank the reviewer for their question, the answer to which we will try to add to the new version of our manuscript. Yes, there are analyses in the literature of computational complexity specific to the use of credal sets, particularly in the context of graphical models and probabilistic inference. Such approaches can be implemented for large datasets, but they often require approximation techniques to be computationally feasible [1, 2, 3 ].
Despite this, credal set approaches can be implemented for large datasets using techniques like parallel processing, distributed computing, and efficient data structures. Similar to Deep Learning-based approaches, utilization of high-performance computing resources, algorithm optimization, and domain-specific adaptations, the computational challenges can be effectively managed. Recent advancements demonstrate the practicality of these approaches. For instance, "Credal-Set Interval Neural Networks" (CreINNs) have shown significant improvements in inference time over variational Bayesian neural networks [4]. Thus, while the computational demands are comparable to those of deep learning-based methods, the robustness and flexibility of credal sets, as demonstrated in recent research, make them a practical and valuable approach [5, 6].
References:
[1] Mauá, Denis Deratani, and Fabio Gagliardi Cozman. "Thirty years of credal networks: Specification, algorithms and complexity." International Journal of Approximate Reasoning 126 (2020): 133-157.
[2] Lienen, Julian, and Eyke Hüllermeier. "Credal self-supervised learning." Advances in Neural Information Processing Systems 34 (2021): 14370-14382.
[3] Mauá, Denis D., et al. "On the complexity of strong and epistemic credal networks." arXiv preprint arXiv:1309.6845 (2013).
[4] Wang, Kaizheng, et al. "CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks." arXiv preprint arXiv:2401.05043 (2024).
[5] Marinescu, Radu, et al. "Credal marginal map." Advances in Neural Information Processing Systems 36 (2024).
[6] Wang, Kaizheng, et al. "Credal Wrapper of Model Averaging for Uncertainty Estimation on Out-Of-Distribution Detection." arXiv preprint arXiv:2405.15047 (2024).