Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have recently achieved strong performance for sequence modeling, most probabilistic forecasting approaches rely on restrictive parametric likelihoods or quantile-based objectives. They can struggle to capture complex joint predictive distributions across multiple correlated time series. This work proposes EnTransformer, a deep generative forecasting framework that integrates engression, a stochastic learning paradigm for modeling conditional distributions, with the expressive sequence modeling capabilities of Transformers. The proposed approach injects stochastic noise into the model representation and optimizes an energy-based scoring objective to directly learn the conditional predictive distribution without imposing parametric assumptions. This design enables EnTransformer to generate coherent multivariate forecast trajectories while preserving Transformers' capacity to effectively model long-range temporal dependencies and cross-series interactions. We evaluate our proposed EnTransformer on several widely used benchmarks for multivariate probabilistic forecasting, including Electricity, Traffic, Solar, Taxi, KDD-cup, and Wikipedia datasets. Experimental results demonstrate that EnTransformer produces well-calibrated probabilistic forecasts and consistently outperforms the benchmark models.

翻译：在能源系统和交通网络等诸多领域的多元时间序列预测问题中，可靠的量化不确定性至关重要。尽管基于Transformer的架构最近在序列建模方面取得了强劲的性能，但大多数概率预测方法依赖于限制性的参数似然或基于分位数的目标函数。这些方法难以捕捉多个相关时间序列之间复杂的联合预测分布。本研究提出了EnTransformer，一个深度生成式预测框架，它将用于建模条件分布的随机学习范式——engression，与Transformer强大的序列建模能力相结合。所提出的方法将随机噪声注入模型表示中，并优化基于能量的评分目标，以直接学习条件预测分布，而无需施加参数假设。这种设计使EnTransformer能够生成连贯的多元预测轨迹，同时保持Transformer有效建模长程时间依赖性和跨序列交互的能力。我们在多个广泛使用的多元概率预测基准数据集上评估了所提出的EnTransformer，包括Electricity、Traffic、Solar、Taxi、KDD-cup和Wikipedia数据集。实验结果表明，EnTransformer能够产生校准良好的概率预测，并持续优于基准模型。