Deep-learning models for traffic data prediction can have superior performance in modeling complex functions using a multi-layer architecture. However, a major drawback of these approaches is that most of these approaches do not offer forecasts with uncertainty estimates, which are essential for traffic operations and control. Without uncertainty estimates, it is difficult to place any level of trust to the model predictions, and operational strategies relying on overconfident predictions can lead to worsening traffic conditions. In this study, we propose a Bayesian recurrent neural network framework for uncertainty quantification in traffic prediction with higher generalizability by introducing spectral normalization to its hidden layers. In our paper, we have shown that normalization alters the training process of deep neural networks by controlling the model's complexity and reducing the risk of overfitting to the training data. This, in turn, helps improve the generalization performance of the model on out-of-distribution datasets. Results demonstrate that spectral normalization improves uncertainty estimates and significantly outperforms both the layer normalization and model without normalization in single-step prediction horizons. This improved performance can be attributed to the ability of spectral normalization to better localize the feature space of the data under perturbations. Our findings are especially relevant to traffic management applications, where predicting traffic conditions across multiple locations is the goal, but the availability of training data from multiple locations is limited. Spectral normalization, therefore, provides a more generalizable approach that can effectively capture the underlying patterns in traffic data without requiring location-specific models.

翻译：深度学习模型通过多层架构建模复杂函数，在交通数据预测中表现出优异性能。然而，这类方法的一个主要缺陷是大多数模型无法提供带有不确定性估计的预测结果，而这对于交通运营与控制至关重要。缺乏不确定性估计会降低对模型预测的信任程度，依赖过度自信的预测所制定的运营策略可能导致交通状况恶化。本研究提出一种贝叶斯循环神经网络框架，通过在其隐藏层引入谱归一化，实现交通预测中不确定性的量化并提升泛化能力。我们证明，归一化通过控制模型复杂度、降低训练数据过拟合风险来改变深度神经网络的训练过程，进而提升模型在分布外数据集上的泛化性能。实验结果表明，在单步预测场景中，谱归一化不仅优化了不确定性估计，其性能也显著优于层归一化及无归一化模型。这种改进归因于谱归一化在数据扰动下能更精准地定位特征空间的能力。本研究结论尤其适用于交通管理应用——尽管此类应用需预测多地点交通状况，但多地点训练数据有限。因此，谱归一化提供了一种无需位置特定模型即可有效捕捉交通数据潜在模式的泛化方法。