Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To make an accurate reconstruction on partially observed traffic data, we assert the importance of characterizing both global and local trends in traffic time series. In the literature, substantial prior works have demonstrated the effectiveness of utilizing low-rankness property of traffic data by matrix/tensor completion models. In this study, we first introduce a Laplacian kernel to temporal regularization for characterizing local trends in traffic time series, which can be formulated in the form of circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the nuclear norm of a circulant matrix and the Laplacian temporal regularization together, which is proved to meet a unified framework that takes a fast Fourier transform solution in a relatively low time complexity. Through extensive experiments on some traffic datasets, we demonstrate the superiority of LCR for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity). The proposed LCR model is an efficient and effective solution to large-scale traffic data imputation over the existing baseline models. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/transdim.

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector autoregression (VAR) model whose coefficient matrices are parameterized by low-rank tensor factorization. Benefiting from the tensor factorization structure, the proposed model can simultaneously achieve model compression and pattern discovery. In particular, the proposed model allows one to characterize nonstationarity and time-varying system behaviors underlying spatiotemporal data. To evaluate the proposed model, extensive experiments are conducted on various spatiotemporal data representing different nonlinear dynamical systems, including fluid dynamics, sea surface temperature, USA surface temperature, and NYC taxi trips. Experimental results demonstrate the effectiveness of modeling spatiotemporal data and characterizing spatial/temporal patterns with the proposed model. In the spatial context, the spatial patterns can be automatically extracted and intuitively characterized by the spatial modes. In the temporal context, the complex time-varying system behaviors can be revealed by the temporal modes in the proposed model. Thus, our model lays an insightful foundation for understanding complex spatiotemporal data in real-world dynamical systems. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/vars.

现代时间序列数据集通常是高维，不完整/稀疏和非组织的。这些属性阻碍了时间序列预测和分析的可扩展和高效解决方案的开发。为了应对这些挑战，我们提出了一个非平稳的时间矩阵分解（NOTMF）模型，其中使用矩阵分解来重建整个时间序列矩阵和矢量自回旋（var）过程，该过程施加在适当差异的时间因子矩阵的副本上。这种方法不仅保留了数据的低级属性，还提供了一致的时间动力。 NOTMF的学习过程涉及两个因子矩阵和VAR系数矩阵集合的优化。为了有效地解决优化问题，我们得出了一个交替的最小化框架，其中使用共轭梯度和最小二乘方法来解决子问题。特别是，使用共轭梯度方法提供了有效的例程，并允许我们在大规模问题上应用NOTMF。通过对Uber运动速度数据集进行的广泛实验，我们证明了NOTMF的卓越准确性和有效性，而不是其他基线模型。我们的结果还证实了解决现实世界中时间序列数据（如时空交通流/速度）的非平稳性的重要性。

我们研究了自然非凸形公式下的不对称矩阵分解问题，并具有任意的过多参数化。考虑了无模型设置，对观察到的矩阵的秩或单数值的假设最小，在该矩阵的秩或奇异值中，全局最优值证明过度拟合。我们表明，带有小随机初始化的香草梯度下降顺序恢复了观察到的矩阵的主要成分。因此，当配备适当的早期停止时，梯度下降会产生观察到的矩阵的最佳低级别近似，而无需显式正则化。我们提供了近似误差，迭代复杂性，初始化大小和步骤大小之间关系的尖锐表征。我们的复杂性界限几乎不含尺寸，并取决于对数近似误差，与先前的工作相比，对步骤和初始化的宽大要求明显更大。我们的理论结果为行为梯度下降提供了准确的预测，显示了与数值实验的良好一致性。

在本文中，我们研究了从同步2D和3D数据共同估计光流量和场景流的问题。以前的方法使用复杂的管道，将联合任务分成独立阶段，或以“早期融合”或“迟到的”方式“的熔断器2D和3D信息。这种单尺寸适合的方法遭受了未能充分利用每个模态的特征的困境，或者最大化模态互补性。为了解决这个问题，我们提出了一个新的端到端框架，称为Camliflow。它由2D和3D分支组成，在特定层之间具有多个双向连接。与以前的工作不同，我们应用基于点的3D分支以更好地提取几何特征，并设计一个对称的学习操作员以保险熔断致密图像特征和稀疏点特征。我们还提出了一种转换，以解决3D-2D投影的非线性问题。实验表明，Camliflow以更少的参数实现了更好的性能。我们的方法在Kitti场景流基准上排名第一，表现出以1/7参数的前一篇文章。代码将可用。

差分方程管理的学习动态对于预测和控制科学和工程系统来说至关重要。神经常规方程（节点）是一种与微分方程集成的深度学习模型，最近是由于其对不规则样本的鲁棒性及其对高维输入的灵活性而流行的学习动态。然而，节点的训练对数值求解器的精度敏感，这使得节点的收敛不稳定，特别是对于不稳定的动态系统。在本文中，为了减少对数值求解器的依赖，我们建议提高节点训练中的监督信号。具体地，我们预先训练神经差分运算符（NDO）以输出衍生物的估计用作额外的监督信号。 NDO在一类基础函数上预先培训，并将这些功能的轨迹样本之间的映射学习到其衍生物。为了利用来自NDO的轨迹信号和估计的衍生工具，我们提出了一种称为NDO-Node的算法，其中损耗函数包含两个术语：真正轨迹样本的适应性以及由输出的估计衍生物的适应度预先训练的NDO。各种动力学的实验表明，我们提出的NDO-Node可以一致地用一个预先训练的NDO来改善预测精度。特别是对于僵硬的杂散，我们观察到与其他正则化方法相比，NDO-Node可以更准确地捕获动态的过渡。

低秩矩阵恢复的现有结果在很大程度上专注于二次损失，这享有有利的性质，例如限制强的强凸/平滑度（RSC / RSM）以及在所有低等级矩阵上的良好调节。然而，许多有趣的问题涉及更一般，非二次损失，这不满足这些属性。对于这些问题，标准的非耦合方法，例如秩约为秩约为预定的梯度下降（A.K.A.迭代硬阈值）和毛刺蒙特罗分解可能具有差的经验性能，并且没有令人满意的理论保证了这些算法的全球和快速收敛。在本文中，我们表明，具有非二次损失的可证实低级恢复中的关键组成部分是规律性投影oracle。该Oracle限制在适当的界限集中迭代到低级矩阵，损耗功能在其上表现良好并且满足一组近似RSC / RSM条件。因此，我们分析配备有这样的甲骨文的（平均）投影的梯度方法，并证明它在全球和线性地收敛。我们的结果适用于广泛的非二次低级估计问题，包括一个比特矩阵感测/完成，个性化排名聚集，以及具有等级约束的更广泛的广义线性模型。

Existing deep learning-based traffic forecasting models are mainly trained with MSE (or MAE) as the loss function, assuming that residuals/errors follow independent and isotropic Gaussian (or Laplacian) distribution for simplicity. However, this assumption rarely holds for real-world traffic forecasting tasks, where the unexplained residuals are often correlated in both space and time. In this study, we propose Spatiotemporal Residual Regularization by modeling residuals with a dynamic (e.g., time-varying) mixture of zero-mean multivariate Gaussian distribution with learnable spatiotemporal covariance matrices. This approach allows us to directly capture spatiotemporally correlated residuals. For scalability, we model the spatiotemporal covariance for each mixture component using a Kronecker product structure, which significantly reduces the number of parameters and computation complexity. We evaluate the performance of the proposed method on a traffic speed forecasting task. Our results show that, by properly modeling residual distribution, the proposed method not only improves the model performance but also provides interpretable structures.

We introduce the MAsked Generative VIdeo Transformer, MAGVIT, to tackle various video synthesis tasks with a single model. We introduce a 3D tokenizer to quantize a video into spatial-temporal visual tokens and propose an embedding method for masked video token modeling to facilitate multi-task learning. We conduct extensive experiments to demonstrate the quality, efficiency, and flexibility of MAGVIT. Our experiments show that (i) MAGVIT performs favorably against state-of-the-art approaches and establishes the best-published FVD on three video generation benchmarks, including the challenging Kinetics-600. (ii) MAGVIT outperforms existing methods in inference time by two orders of magnitude against diffusion models and by 60x against autoregressive models. (iii) A single MAGVIT model supports ten diverse generation tasks and generalizes across videos from different visual domains. The source code and trained models will be released to the public at https://magvit.cs.cmu.edu.

Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e., the score function, is not properly defined for discrete spaces. This makes it non-trivial to adapt \textcolor{\cdiff}{the score-based modeling} to categorical data. In this paper, we extend diffusion models to discrete variables by introducing a stochastic jump process where the reverse process denoises via a continuous-time Markov chain. This formulation admits an analytical simulation during backward sampling. To learn the reverse process, we extend score matching to general categorical data and show that an unbiased estimator can be obtained via simple matching of the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.