让神经网络同时预测不确定性的均值和方差，提升回归任务表现。
On weight and variance uncertainty in neural networks for regression tasks
- 在贝叶斯神经网络中显式建模方差不确定性，而非固定方差。
- 在函数逼近和核糖黄素基因数据集上，显著提升泛化性能。
- 适用于对预测置信度有要求的回归场景，如生物信息学。
本文研究了贝叶斯神经网络在回归任务中权重不确定性的建模问题，扩展了Blundell等人（2015）的框架，引入方差不确定性建模。通过在方差上建立完整的后验分布，模型相比固定方差的方法实现了更好的泛化能力。我们在函数逼近实验和riboflavin基因数据集上验证了该方法的有效性，涵盖全连接网络与含丢弃的网络，并分别使用高斯先验和尖刺-平滑先验，系统评估了不同架构下方差不确定性对性能的影响。
原文摘要 · Abstract (English)
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.
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