Reconstructing Fine-Grained Network Data using Autoencoder Architectures with Domain Knowledge Penalties

The ability to reconstruct fine-grained network session data, including individual packets, from coarse-grained feature vectors is crucial for improving network security models. However, the large-scale collection and storage of raw network traffic pose significant challenges, particularly for capturing rare cyberattack samples. These challenges hinder the ability to retain comprehensive datasets for model training and future threat detection. To address this, we propose a machine learning approach guided by formal methods to encode and reconstruct network data. Our method employs autoencoder models with domain-informed penalties to impute PCAP session headers from structured feature representations. Experimental results demonstrate that incorporating domain knowledge through constraint-based loss terms significantly improves reconstruction accuracy, particularly for categorical features with session-level encodings. By enabling efficient reconstruction of detailed network sessions, our approach facilitates data-efficient model training while preserving privacy and storage efficiency.

MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm

Imputation of random or non-random missing data is a long-standing research topic and a crucial application for Intelligent Transportation Systems (ITS). However, with the advent of modern communication technologies such as Global Satellite Navigation Systems (GNSS), traffic data collection has outpaced traditional methods, introducing new challenges in random missing value imputation and increasing demands for spatiotemporal dependency modelings. To address these issues, we propose a novel spatiotemporal traffic imputation method, Multimode Nonlinear Transformed Tensor Nuclear Norm (MNT-TNN), grounded in the Transform-based Tensor Nuclear Norm (TTNN) optimization framework which exhibits efficient mathematical representations and theoretical guarantees for the recovery of random missing values. Specifically, we strictly extend the single-mode transform in TTNN to a multimode transform with nonlinear activation, effectively capturing the intrinsic multimode spatiotemporal correlations and low-rankness of the traffic tensor, represented as location $\times$ location $\times$ time. To solve the nonconvex optimization problem, we design a proximal alternating minimization (PAM) algorithm with theoretical convergence guarantees. We suggest an Augmented Transform-based Tensor Nuclear Norm Families (ATTNNs) framework to enhance the imputation results of TTNN techniques, especially at very high miss rates. Extensive experiments on real datasets demonstrate that our proposed MNT-TNN and ATTNNs can outperform the compared state-of-the-art imputation methods, completing the benchmark of random missing traffic value imputation.

Effective and Efficient Cross-City Traffic Knowledge Transfer A Privacy-Preserving Perspective

Traffic prediction targets forecasting future traffic conditions using historical traffic data, serving a critical role in urban computing and transportation management. To mitigate the scarcity of traffic data while maintaining data privacy, numerous Federated Traffic Knowledge Transfer (FTT) approaches have been developed, which use transfer learning and federated learning to transfer traffic knowledge from data-rich cities to data-scarce cities, enhancing traffic prediction capabilities for the latter. However, current FTT approaches face challenges such as privacy leakage, cross-city data distribution discrepancies, low data quality, and inefficient knowledge transfer, limiting their privacy protection, effectiveness, robustness, and efficiency in real-world applications. To this end, we propose FedTT, an effective, efficient, and privacy-aware cross-city traffic knowledge transfer framework that transforms the traffic data domain from the data-rich cities and trains traffic models using the transformed data for the data-scarce cities. First, to safeguard data privacy, we propose a traffic secret transmission method that securely transmits and aggregates traffic domain-transformed data from source cities using a lightweight secret aggregation approach. Second, to mitigate the impact of traffic data distribution discrepancies on model performance, we introduce a traffic domain adapter to uniformly transform traffic data from the source cities' domains to that of the target city. Third, to improve traffic data quality, we design a traffic view imputation method to fill in and predict missing traffic data. Finally, to enhance transfer efficiency, FedTT is equipped with a federated parallel training method that enables the simultaneous training of multiple modules. Extensive experiments using 4 real-life datasets demonstrate that FedTT outperforms the 14 state-of-the-art baselines.

SUSTeR: Sparse Unstructured Spatio Temporal Reconstruction on Traffic Prediction

Mining spatio-temporal correlation patterns for traffic prediction is a well-studied field. However, most approaches are based on the assumption of the availability of and accessibility to a sufficiently dense data source, which is rather the rare case in reality. Traffic sensors in road networks are generally highly sparse in their distribution: fleet-based traffic sensing is sparse in space but also sparse in time. There are also other traffic application, besides road traffic, like moving objects in the marine space, where observations are sparsely and arbitrarily distributed in space. In this paper, we tackle the problem of traffic prediction on sparse and spatially irregular and non-deterministic traffic observations. We draw a border between imputations and this work as we consider high sparsity rates and no fixed sensor locations. We advance correlation mining methods with a Sparse Unstructured Spatio Temporal Reconstruction (SUSTeR) framework that reconstructs traffic states from sparse non-stationary observations. For the prediction the framework creates a hidden context traffic state which is enriched in a residual fashion with each observation. Such an assimilated hidden traffic state can be used by existing traffic prediction methods to predict future traffic states. We query these states with query locations from the spatial domain.

CoSTI: Consistency Models for (a faster) Spatio-Temporal Imputation

Multivariate Time Series Imputation (MTSI) is crucial for many applications, such as healthcare monitoring and traffic management, where incomplete data can compromise decision-making. Existing state-of-the-art methods, like Denoising Diffusion Probabilistic Models (DDPMs), achieve high imputation accuracy; however, they suffer from significant computational costs and are notably time-consuming due to their iterative nature. In this work, we propose CoSTI, an innovative adaptation of Consistency Models (CMs) for the MTSI domain. CoSTI employs Consistency Training to achieve comparable imputation quality to DDPMs while drastically reducing inference times, making it more suitable for real-time applications. We evaluate CoSTI across multiple datasets and missing data scenarios, demonstrating up to a 98% reduction in imputation time with performance on par with diffusion-based models. This work bridges the gap between efficiency and accuracy in generative imputation tasks, providing a scalable solution for handling missing data in critical spatio-temporal systems.

Boundary-enhanced time series data imputation with long-term dependency diffusion models

Data imputation is crucial for addressing challenges posed by missing values in multivariate time series data across various fields, such as healthcare, traffic, and economics, and has garnered significant attention. Among various methods, diffusion model-based approaches show notable performance improvements. However, existing methods often cause disharmonious boundaries between missing and known regions and overlook long-range dependencies in missing data estimation, leading to suboptimal results. To address these issues, we propose a Diffusion-based time Series Data Imputation (DSDI) framework. We develop a weight-reducing injection strategy that incorporates the predicted values of missing points with reducing weights into the reverse diffusion process to mitigate boundary inconsistencies. Further, we introduce a multi-scale S4-based U-Net, which combines hierarchical information from different levels via multi-resolution integration to capture long-term dependencies. Experimental results demonstrate that our model outperforms existing imputation methods.

An Experimental Evaluation of Imputation Models for Spatial-Temporal Traffic Data

Traffic data imputation is a critical preprocessing step in intelligent transportation systems, enabling advanced transportation services. Despite significant advancements in this field, selecting the most suitable model for practical applications remains challenging due to three key issues: 1) incomprehensive consideration of missing patterns that describe how data loss along spatial and temporal dimensions, 2) the lack of test on standardized datasets, and 3) insufficient evaluations. To this end, we first propose practice-oriented taxonomies for missing patterns and imputation models, systematically identifying all possible forms of real-world traffic data loss and analyzing the characteristics of existing models. Furthermore, we introduce a unified benchmarking pipeline to comprehensively evaluate 10 representative models across various missing patterns and rates. This work aims to provide a holistic understanding of traffic data imputation research and serve as a practical guideline.

RDPI: A Refine Diffusion Probability Generation Method for Spatiotemporal Data Imputation

Spatiotemporal data imputation plays a crucial role in various fields such as traffic flow monitoring, air quality assessment, and climate prediction. However, spatiotemporal data collected by sensors often suffer from temporal incompleteness, and the sparse and uneven distribution of sensors leads to missing data in the spatial dimension. Among existing methods, autoregressive approaches are prone to error accumulation, while simple conditional diffusion models fail to adequately capture the spatiotemporal relationships between observed and missing data. To address these issues, we propose a novel two-stage Refined Diffusion Probability Impuation (RDPI) framework based on an initial network and a conditional diffusion model. In the initial stage, deterministic imputation methods are used to generate preliminary estimates of the missing data. In the refinement stage, residuals are treated as the diffusion target, and observed values are innovatively incorporated into the forward process. This results in a conditional diffusion model better suited for spatiotemporal data imputation, bridging the gap between the preliminary estimates and the true values. Experiments on multiple datasets demonstrate that RDPI not only achieves state-of-the-art imputation accuracy but also significantly reduces sampling computational costs.

Navigating Data Corruption in Machine Learning: Balancing Quality, Quantity, and Imputation Strategies

Data corruption, including missing and noisy data, poses significant challenges in real-world machine learning. This study investigates the effects of data corruption on model performance and explores strategies to mitigate these effects through two experimental setups: supervised learning with NLP tasks (NLP-SL) and deep reinforcement learning for traffic signal optimization (Signal-RL). We analyze the relationship between data corruption levels and model performance, evaluate the effectiveness of data imputation methods, and assess the utility of enlarging datasets to address data corruption. Our results show that model performance under data corruption follows a diminishing return curve, modeled by the exponential function. Missing data, while detrimental, is less harmful than noisy data, which causes severe performance degradation and training instability, particularly in sequential decision-making tasks like Signal-RL. Imputation strategies involve a trade-off: they recover missing information but may introduce noise. Their effectiveness depends on imputation accuracy and corruption ratio. We identify distinct regions in the imputation advantage heatmap, including an "imputation advantageous corner" and an "imputation disadvantageous edge" and classify tasks as "noise-sensitive" or "noise-insensitive" based on their decision boundaries. Furthermore, we find that increasing dataset size mitigates but cannot fully overcome the effects of data corruption. The marginal utility of additional data diminishes as corruption increases. An empirical rule emerges: approximately 30% of the data is critical for determining performance, while the remaining 70% has minimal impact. These findings provide actionable insights into data preprocessing, imputation strategies, and data collection practices, guiding the development of robust machine learning systems in noisy environments.

FastSTI: A Fast Conditional Pseudo Numerical Diffusion Model for Spatio-temporal Traffic Data Imputation

High-quality spatiotemporal traffic data is crucial for intelligent transportation systems (ITS) and their data-driven applications. Inevitably, the issue of missing data caused by various disturbances threatens the reliability of data acquisition. Recent studies of diffusion probability models have demonstrated the superiority of deep generative models in imputation tasks by precisely capturing the spatio-temporal correlation of traffic data. One drawback of diffusion models is their slow sampling/denoising process. In this work, we aim to accelerate the imputation process while retaining the performance. We propose a fast conditional diffusion model for spatiotemporal traffic data imputation (FastSTI). To speed up the process yet, obtain better performance, we propose the application of a high-order pseudo-numerical solver. Our method further revs the imputation by introducing a predefined alignment strategy of variance schedule during the sampling process. Evaluating FastSTI on two types of real-world traffic datasets (traffic speed and flow) with different missing data scenarios proves its ability to impute higher-quality samples in only six sampling steps, especially under high missing rates (60\% $\sim$ 90\%). The experimental results illustrate a speed-up of $\textbf{8.3} \times$ faster than the current state-of-the-art model while achieving better performance.