S2312
Physics - Machine learning and AI algorithms
ESTRO 2026
Figure 1. Each Unet consisted of a single encoder and a pair of decoders; one to calculated the dose and the other to calculate the aleatoric uncertainty. To create a Bayesian network for estimating epistemic uncertainty each weight in the network was replaced by a continuous, radial distribution to ensure that the distribution had continuous support [1]. Normal distributions were used for weight priors. The variance decoder component used fixed weights. Dose was modelled using a beta distribution, parametrised as a uni-modal distribution, ensuring the predicted dose lay between zero and Dmax. The loss function was the ELBO (Evidence Lower Bound) as expressed in [2]. The epistemic and aleatoric uncertainty were estimated to using the law of total variance from multiple draws of the posterior.
Conclusion: Bayesian neural networks can be used to estimate both epistemic and aleatoric uncertainty. This information can be visualised by planners to show where models are less certain in their prediction and quantify prediction uncertainty. References: [1] Farquhar, S., Osborne, M. A., & Gal, Y. (2020, June). Radial bayesian neural networks: Beyond discrete support in large-scale bayesian deep learning. In International Conference on Artificial Intelligence and Statistics (pp. 1352-1362). PMLR.[2] Blundell, C., Cornebise, J., Kavukcuoglu, K., & Wierstra, D. (2015, June). Weight uncertainty in neural network. In International conference on machine learning (pp. 1613-1622). PMLR. Keywords: uncertainty, bayesian network, dose
Results: Figure 2 shows rectum DVHs created by samples from the posterior distribution. The colour wash shows a map of the epistemic uncertainty in the planning system, illustrating to a planner where the model is more-or-less confident in its prediction. The epistemic uncertainty tended to dominate and was largest in a ring around the PTV as shown in Figure 2. The uncertainty in relative rectum V40Gy due to the model was 1.5% and the uncertainty in PTV 48Gy D98% was 1.2Gy.
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