Lijun Sun

Xinyu Chen, Chengyuan Zhang, Xiaoxu Chen et al.

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.

Xinyu Chen, Zhanhong Cheng, HanQin Cai et al.

Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To perform efficient learning and accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in time series. In the literature, substantial works have demonstrated the effectiveness of utilizing the low-rank 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 as a circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the circulant matrix nuclear norm and the Laplacian kernelized temporal regularization together, which is proved to meet a unified framework that has a fast Fourier transform (FFT) solution in log-linear time complexity. Through extensive experiments on several traffic datasets, we demonstrate the superiority of LCR over several baseline models for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity) and reconstructing sparse speed fields of vehicular traffic flow. The proposed LCR model is also an efficient solution to large-scale traffic data imputation over the existing imputation models.

Fan Wu, Zhanhong Cheng, Huiyu Chen et al.

Accurately monitoring road traffic state is crucial for various applications, including travel time prediction, traffic control, and traffic safety. However, the lack of sensors often results in incomplete traffic state data, making it challenging to obtain reliable information for decision-making. This paper proposes a novel method for imputing traffic state data using Gaussian processes (GP) to address this issue. We propose a kernel rotation re-parametrization scheme that transforms a standard isotropic GP kernel into an anisotropic kernel, which can better model the congestion propagation in traffic flow data. The model parameters can be estimated by statistical inference using data from sparse probe vehicles or loop detectors. Moreover, the rotated GP method provides statistical uncertainty quantification for the imputed traffic state, making it more reliable. We also extend our approach to a multi-output GP, which allows for simultaneously estimating the traffic state for multiple lanes. We evaluate our method using real-world traffic data from the Next Generation simulation (NGSIM) and HighD programs, along with simulated data representing a traffic bottleneck scenario. Considering current and future mixed traffic of connected vehicles (CVs) and human-driven vehicles (HVs), we experiment with the traffic state estimation (TSE) scheme from 5% to 50% available trajectories, mimicking different CV penetration rates in a mixed traffic environment. We also test the traffic state estimation when traffic flow information is obtained from loop detectors. The results demonstrate the adaptability of our TSE method across different CV penetration rates and types of detectors, achieving state-of-the-art accuracy in scenarios with sparse observation rates.

Vincent Zhihao Zheng, Seongjin Choi, Lijun Sun

This paper proposes a dynamic regression (DR) framework that enhances existing deep spatiotemporal models by incorporating structured learning for the error process in traffic forecasting. The framework relaxes the assumption of time independence by modeling the error series of the base model (i.e., a well-established traffic forecasting model) using a matrix-variate autoregressive (AR) model. The AR model is integrated into training by redesigning the loss function. The newly designed loss function is based on the likelihood of a non-isotropic error term, enabling the model to generate probabilistic forecasts while preserving the original outputs of the base model. Importantly, the additional parameters introduced by the DR framework can be jointly optimized alongside the base model. Evaluation on state-of-the-art (SOTA) traffic forecasting models using speed and flow datasets demonstrates improved performance, with interpretable AR coefficients and spatiotemporal covariance matrices enhancing the understanding of the model.

Zhanjiang Yang, Lijun Sun, Jiawei Dong et al.

Reconstructing hyperspectral images (HSIs) from RGB inputs provides a cost-effective alternative to hyperspectral cameras, but reconstructing high-dimensional spectra from three channels is inherently ill-posed. Existing methods typically directly regress RGB-to-HSI mappings using large attention networks, which are computationally expensive and handle ill-posedness only implicitly. We propose MCGA, a Mixture-of-Codebooks with Grayscale-aware Attention framework that explicitly addresses these challenges using spectral priors and photometric consistency. MCGA first learns transferable spectral priors via a mixture-of-codebooks (MoC) from heterogeneous HSI datasets, then aligns RGB features with these priors through grayscale-aware photometric attention (GANet). Efficiency and robustness are further improved via top-K attention design and test-time adaptation (TTA). Experiments on benchmarks and real-world data demonstrate the state-of-the-art accuracy, strong cross-dataset generalization, and 4-5x faster inference. Codes will be available once acceptance at https://github.com/Fibonaccirabbit/MCGA.

Vincent Zhihao Zheng, Lijun Sun

Multivariate Gaussian (MVG) distributions are central to modeling correlated continuous variables in probabilistic forecasting. Neural forecasting models typically parameterize the mean vector and covariance matrix of the distribution using neural networks, optimizing with the log-score (negative log-likelihood) as the loss function. However, the sensitivity of the log-score to outliers can lead to significant errors in the presence of anomalies. Drawing on the continuous ranked probability score (CRPS) for univariate distributions, we propose MVG-CRPS, a strictly proper scoring rule for MVG distributions. MVG-CRPS admits a closed-form expression in terms of neural network outputs, thereby integrating seamlessly into deep learning frameworks. Experiments on real-world datasets across multivariate autoregressive and univariate sequence-to-sequence (Seq2Seq) forecasting tasks show that MVG-CRPS improves robustness, accuracy, and uncertainty quantification in probabilistic forecasting.

Vincent Zhihao Zheng, Lijun Sun

Accurately modeling the correlation structure of errors is critical for reliable uncertainty quantification in probabilistic time series forecasting. While recent deep learning models for multivariate time series have developed efficient parameterizations for time-varying contemporaneous covariance, but they often assume temporal independence of errors for simplicity. However, real-world data often exhibit significant error autocorrelation and cross-lag correlation due to factors such as missing covariates. In this paper, we introduce a plug-and-play method that learns the covariance structure of errors over multiple steps for autoregressive models with Gaussian-distributed errors. To ensure scalable inference and computational efficiency, we model the contemporaneous covariance using a low-rank-plus-diagonal parameterization and capture cross-covariance through a group of independent latent temporal processes. The learned covariance matrix is then used to calibrate predictions based on observed residuals. We evaluate our method on probabilistic models built on RNNs and Transformer architectures, and the results confirm the effectiveness of our approach in improving predictive accuracy and uncertainty quantification without significantly increasing the parameter size.

Chengyuan Zhang, Kehua Chen, Meixin Zhu et al.

Learning and understanding car-following (CF) behaviors are crucial for microscopic traffic simulation. Traditional CF models, though simple, often lack generalization capabilities, while many data-driven methods, despite their robustness, operate as "black boxes" with limited interpretability. To bridge this gap, this work introduces a Bayesian Matrix Normal Mixture Regression (MNMR) model that simultaneously captures feature correlations and temporal dynamics inherent in CF behaviors. This approach is distinguished by its separate learning of row and column covariance matrices within the model framework, offering an insightful perspective into the human driver decision-making processes. Through extensive experiments, we assess the model's performance across various historical steps of inputs, predictive steps of outputs, and model complexities. The results consistently demonstrate our model's adeptness in effectively capturing the intricate correlations and temporal dynamics present during CF. A focused case study further illustrates the model's outperforming interpretability of identifying distinct operational conditions through the learned mean and covariance matrices. This not only underlines our model's effectiveness in understanding complex human driving behaviors in CF scenarios but also highlights its potential as a tool for enhancing the interpretability of CF behaviors in traffic simulations and autonomous driving systems.