We investigate the problem of weight uncertainty originally proposed by [Blundell et al. (2015). Weight uncertainty in neural networks. In International conference on machine learning, 1613-1622, PMLR.] in the context of neural networks designed for regression tasks, and we extend their framework by incorporating variance uncertainty into the model. Our analysis demonstrates that explicitly modeling uncertainty in the variance parameter can significantly enhance the predictive performance of Bayesian neural networks. By considering a full posterior distribution over the variance, the model achieves improved generalization compared to approaches that treat variance as fixed or deterministic. We evaluate the generalization capability of our proposed approach through a function approximation example and further validate it on the riboflavin genetic dataset. Our exploration encompasses both fully connected dense networks and dropout neural networks, employing Gaussian and spike-and-slab priors respectively for the network weights, providing a comprehensive assessment of how variance uncertainty affects model performance across different architectural choices.

翻译：本研究探讨了[Blundell等人(2015)在《国际机器学习会议》中提出的"神经网络中的权重不确定性"问题，并将其框架扩展到回归任务专用的神经网络中，通过将方差不确定性纳入模型进行拓展。我们的分析表明，显式建模方差参数的不确定性能够显著提升贝叶斯神经网络的预测性能。通过考虑方差参数的完整后验分布，相较于将方差视为固定或确定性的方法，该模型实现了更好的泛化能力。我们通过函数逼近示例评估了所提方法的泛化性能，并在核黄素基因数据集上进行了进一步验证。本研究涵盖了全连接密集网络和dropout神经网络两种架构，分别对网络权重采用高斯先验和尖峰-平板先验，系统评估了方差不确定性在不同架构选择中对模型性能的影响。