In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion probabilistic models, a class of latent variable models closely connected to score matching and energy-based methods. Our model learns gradients by optimizing a variational bound on the data likelihood and at inference time converts white noise into a sample of the distribution of interest through a Markov chain using Langevin sampling. We demonstrate experimentally that the proposed autoregressive denoising diffusion model is the new state-of-the-art multivariate probabilistic forecasting method on real-world data sets with thousands of correlated dimensions. We hope that this method is a useful tool for practitioners and lays the foundation for future research in this area.

本研究提出了一种基于 TimeGrad 的自回归模型，用于多元概率时间序列预测，该模型在每个时间步长从数据分布中采样，通过估计梯度进行采样，采用扩散概率模型，优化可变界，通过 Langevin 采样将白噪声转换为感兴趣的分布样本，在实验中表明，该模型是当前实现多元概率预测的最佳方法之一，可实际应用于数千个相关维度的真实数据集。

自回归去噪扩散模型用于多元概率时间序列预测