MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecasting

In probabilistic time series forecasting, the multivariate Gaussian (MVG) distribution is widely used as predictive distribution for correlated continuous random variables. Current deep probabilistic models typically employ neural networks to parameterize the mean vector and covariance matrix of the distribution, with log-score (i.e., negative log-likelihood) as the default loss function. However, log-score is highly sensitive to outliers, leading to significant errors when anomalies are present in the data. Motivated by the use of the continuous ranked probability score (CRPS) in learning univariate distributions, we propose a robust loss function specifically designed for high-dimensional MVG outputs. The proposed MVG-CRPS loss function has a closed-form expression based on the neural network outputs, making it easily integrable into deep learning models. We evaluate MVG-CRPS on two probabilistic forecasting tasks -- multivariate autoregressive and univariate sequence-to-sequence (Seq2Seq) forecasting -- both involving observations following MVG distribution. Experimental results on real-world datasets demonstrate that MVG-CRPS achieves both robustness and efficiency, offering enhanced accuracy and uncertainty quantification in probabilistic forecasting.

A Gentle Introduction and Tutorial on Deep Generative Models in Transportation Research

Deep Generative Models (DGMs) have rapidly advanced in recent years, becoming essential tools in various fields due to their ability to learn complex data distributions and generate synthetic data. Their importance in transportation research is increasingly recognized, particularly for applications like traffic data generation, prediction, and feature extraction. This paper offers a comprehensive introduction and tutorial on DGMs, with a focus on their applications in transportation. It begins with an overview of generative models, followed by detailed explanations of fundamental models, a systematic review of the literature, and practical tutorial code to aid implementation. The paper also discusses current challenges and opportunities, highlighting how these models can be effectively utilized and further developed in transportation research. This paper serves as a valuable reference, guiding researchers and practitioners from foundational knowledge to advanced applications of DGMs in transportation research.

Communication-Aware Reinforcement Learning for Cooperative Adaptive Cruise Control

Cooperative Adaptive Cruise Control (CACC) plays a pivotal role in enhancing traffic efficiency and safety in Connected and Autonomous Vehicles (CAVs). Reinforcement Learning (RL) has proven effective in optimizing complex decision-making processes in CACC, leading to improved system performance and adaptability. Among RL approaches, Multi-Agent Reinforcement Learning (MARL) has shown remarkable potential by enabling coordinated actions among multiple CAVs through Centralized Training with Decentralized Execution (CTDE). However, MARL often faces scalability issues, particularly when CACC vehicles suddenly join or leave the platoon, resulting in performance degradation. To address these challenges, we propose Communication-Aware Reinforcement Learning (CA-RL). CA-RL includes a communication-aware module that extracts and compresses vehicle communication information through forward and backward information transmission modules. This enables efficient cyclic information propagation within the CACC traffic flow, ensuring policy consistency and mitigating the scalability problems of MARL in CACC. Experimental results demonstrate that CA-RL significantly outperforms baseline methods in various traffic scenarios, achieving superior scalability, robustness, and overall system performance while maintaining reliable performance despite changes in the number of participating vehicles.

Link Representation Learning for Probabilistic Travel Time Estimation

Travel time estimation is a crucial application in navigation apps and web mapping services. Current deterministic and probabilistic methods primarily focus on modeling individual trips, assuming independence among trips. However, in real-world scenarios, we often observe strong inter-trip correlations due to factors such as weather conditions, traffic management, and road works. In this paper, we propose to model trip-level link travel time using a Gaussian hierarchical model, which can characterize both inter-trip and intra-trip correlations. The joint distribution of travel time of multiple trips becomes a multivariate Gaussian parameterized by learnable link representations. To effectively use the sparse GPS trajectories, we also propose a data augmentation method based on trip sub-sampling, which allows for fine-grained gradient backpropagation in learning link representations. During inference, we estimate the probability distribution of the travel time of a queried trip conditional on the completed trips that are spatiotemporally adjacent. We refer to the overall framework as ProbTTE. We evaluate ProbTTE on two real-world GPS trajectory datasets, and the results demonstrate its superior performance compared to state-of-the-art deterministic and probabilistic baselines. Additionally, we find that the learned link representations align well with the physical geometry of the network, making them suitable as input for other applications.

Learning Car-Following Behaviors Using Bayesian Matrix Normal Mixture Regression

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.

Multivariate Probabilistic Time Series Forecasting with Correlated Errors

Modeling the correlations among errors is closely associated with how accurately the model can quantify predictive uncertainty in probabilistic time series forecasting. Recent multivariate models have made significant progress in accounting for contemporaneous correlations among errors, while a common assumption on these errors is that they are temporally independent for the sake of statistical simplicity. However, real-world observations often deviate from this assumption, since errors usually exhibit substantial autocorrelation due to various factors such as the exclusion of temporally correlated covariates. In this work, we propose an efficient method, based on a low-rank-plus-diagonal parameterization of the covariance matrix, which can effectively characterize the autocorrelation of errors. The proposed method possesses several desirable properties: the complexity does not scale with the number of time series, the resulting covariance can be used for calibrating predictions, and it can seamlessly integrate with any model with Gaussian-distributed errors. We empirically demonstrate these properties using two distinct neural forecasting models-GPVar and Transformer. Our experimental results confirm the effectiveness of our method in enhancing predictive accuracy and the quality of uncertainty quantification on multiple real-world datasets.

Rethinking Urban Mobility Prediction: A Super-Multivariate Time Series Forecasting Approach

Long-term urban mobility predictions play a crucial role in the effective management of urban facilities and services. Conventionally, urban mobility data has been structured as spatiotemporal videos, treating longitude and latitude grids as fundamental pixels. Consequently, video prediction methods, relying on Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), have been instrumental in this domain. In our research, we introduce a fresh perspective on urban mobility prediction. Instead of oversimplifying urban mobility data as traditional video data, we regard it as a complex multivariate time series. This perspective involves treating the time-varying values of each grid in each channel as individual time series, necessitating a thorough examination of temporal dynamics, cross-variable correlations, and frequency-domain insights for precise and reliable predictions. To address this challenge, we present the Super-Multivariate Urban Mobility Transformer (SUMformer), which utilizes a specially designed attention mechanism to calculate temporal and cross-variable correlations and reduce computational costs stemming from a large number of time series. SUMformer also employs low-frequency filters to extract essential information for long-term predictions. Furthermore, SUMformer is structured with a temporal patch merge mechanism, forming a hierarchical framework that enables the capture of multi-scale correlations. Consequently, it excels in urban mobility pattern modeling and long-term prediction, outperforming current state-of-the-art methods across three real-world datasets.

A Critical Perceptual Pre-trained Model for Complex Trajectory Recovery

The trajectory on the road traffic is commonly collected at a low sampling rate, and trajectory recovery aims to recover a complete and continuous trajectory from the sparse and discrete inputs. Recently, sequential language models have been innovatively adopted for trajectory recovery in a pre-trained manner: it learns road segment representation vectors, which will be used in the downstream tasks. However, existing methods are incapable of handling complex trajectories: when the trajectory crosses remote road segments or makes several turns, which we call critical nodes, the quality of learned representations deteriorates, and the recovered trajectories skip the critical nodes. This work is dedicated to offering a more robust trajectory recovery for complex trajectories. Firstly, we define the trajectory complexity based on the detour score and entropy score and construct the complexity-aware semantic graphs correspondingly. Then, we propose a Multi-view Graph and Complexity Aware Transformer (MGCAT) model to encode these semantics in trajectory pre-training from two aspects: 1) adaptively aggregate the multi-view graph features considering trajectory pattern, and 2) higher attention to critical nodes in a complex trajectory. Such that, our MGCAT is perceptual when handling the critical scenario of complex trajectories. Extensive experiments are conducted on large-scale datasets. The results prove that our method learns better representations for trajectory recovery, with 5.22% higher F1-score overall and 8.16% higher F1-score for complex trajectories particularly. The code is available at https://github.com/bonaldli/ComplexTraj.

Choose A Table: Tensor Dirichlet Process Multinomial Mixture Model with Graphs for Passenger Trajectory Clustering

Passenger clustering based on trajectory records is essential for transportation operators. However, existing methods cannot easily cluster the passengers due to the hierarchical structure of the passenger trip information, including multiple trips within each passenger and multi-dimensional information about each trip. Furthermore, existing approaches rely on an accurate specification of the clustering number to start. Finally, existing methods do not consider spatial semantic graphs such as geographical proximity and functional similarity between the locations. In this paper, we propose a novel tensor Dirichlet Process Multinomial Mixture model with graphs, which can preserve the hierarchical structure of the multi-dimensional trip information and cluster them in a unified one-step manner with the ability to determine the number of clusters automatically. The spatial graphs are utilized in community detection to link the semantic neighbors. We further propose a tensor version of Collapsed Gibbs Sampling method with a minimum cluster size requirement. A case study based on Hong Kong metro passenger data is conducted to demonstrate the automatic process of cluster amount evolution and better cluster quality measured by within-cluster compactness and cross-cluster separateness. The code is available at https://github.com/bonaldli/TensorDPMM-G.

Shareable Driving Style Learning and Analysis with a Hierarchical Latent Model

Driving style is usually used to characterize driving behavior for a driver or a group of drivers. However, it remains unclear how one individual's driving style shares certain common grounds with other drivers. Our insight is that driving behavior is a sequence of responses to the weighted mixture of latent driving styles that are shareable within and between individuals. To this end, this paper develops a hierarchical latent model to learn the relationship between driving behavior and driving styles. We first propose a fragment-based approach to represent complex sequential driving behavior, allowing for sufficiently representing driving behavior in a low-dimension feature space. Then, we provide an analytical formulation for the interaction of driving behavior and shareable driving style with a hierarchical latent model by introducing the mechanism of Dirichlet allocation. Our developed model is finally validated and verified with 100 drivers in naturalistic driving settings with urban and highways. Experimental results reveal that individuals share driving styles within and between them. We also analyzed the influence of personalities (e.g., age, gender, and driving experience) on driving styles and found that a naturally aggressive driver would not always keep driving aggressively (i.e., could behave calmly sometimes) but with a higher proportion of aggressiveness than other types of drivers.