arXiv subjects

Christian S. Jensen

Publications and source records attributed to Christian S. Jensen.

At least 19 recordsLinked to original sources

arXiv2026

DGCPath: Distribution-Aware Generative Contrastive Framework for Self-supervised Path Representation Learning -- Extended Version

Due to the proliferation of vehicle trajectory data enabled by advanced sensing technologies, path representation learning has become a pivotal task in intelligent transportation systems. Although existing self-supervised approaches have achieved promising performance, their dependence on deterministic contrastive learning paradigms and handcrafted view augmentation strategies inherently restricts their cross-scenario generalization capabilities. To address these limitations, we present DGCPath, an innovative Distribution-aware Generative Contrastive learning framework for Path representation. This framework establishes a synergistic connection between generative modeling and distributional contrastive learning, enabling the acquisition of robust and transferable feature embeddings. Specifically, our framework incorporates: (1) a diffusion-based view generator that autonomously produces semantically coherent yet diverse trajectory views from Gaussian noise; (2) a variational contrastive mechanism that enforces latent feature alignment at the distribution level, transcending conventional instance-wise consistency; and (3) a novel generative cross-supervision module that reinforces view-level consistency through cross-view reconstruction learning. Comprehensive evaluations on three real-world trajectory datasets demonstrate that DGCPath outperforms state-of-the-art baselines on two distinct downstream tasks, validating its enhanced generalization capability and representation effectiveness.

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arXiv2026

TSMini: A Simple Yet Highly Effective Trajectory Similarity Learning Model

Trajectory similarity is fundamental to many spatio-temporal data mining applications. Recent studies propose deep learning models to approximate conventional trajectory similarity measures, exploiting their fast inference time once trained. Although efficient inference has been reported, challenges remain in similarity approximation accuracy due to difficulties in trajectory granularity modeling and in exploiting similarity signals in training data. To fill this gap, we propose TSMini, a highly effective trajectory similarity model with a sub-view modeling mechanism and a k nearest neighbor-based loss. The former enables learning multi-granularity trajectory patterns, while the latter guides TSMini to learn not only absolute similarity values between trajectories but also their relative similarity ranks. Together, these innovations enable highly accurate trajectory similarity approximation. Experiments show that TSMini outperforms the state-of-the-art models by 15% on average when learning widely used trajectory similarity measures.

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arXiv2026

REFINE: Trajectory Representation Learning via Closed-Loop Transcription -- Extended Version

Trajectory representation learning underpins a wide range of trajectory analytics tasks; however, most existing self-supervised approaches, whether discriminative or generative, adopt an open-loop paradigm, relying on fixed data augmentations or random masking without feedback, which limits their ability to generalize and scale. We propose REFINE, a simple yet effective Representation lEarning Framework vIa closed-loop traNscription rEfinement for trajectory data. Drawing upon feedback control theory, REFINE tightly couples road-network-aware generative reconstruction with feedback-driven contrastive learning, enabling the model to capture fine-grained local movement semantics and global spatio-temporal dependencies without manually designed augmentation views. We further provide a control-theoretic analysis that establishes convergence guarantees for the proposed closed-loop optimization. Extensive experiments on four real-world datasets demonstrate that REFINE consistently outperforms state-of-the-art methods across multiple downstream tasks while remaining computationally efficient and scalable. This paper is an extended version of REFINE: Trajectory Representation Learning via Closed-Loop Transcription, to appear in KDD 2026.

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arXiv2026

VTRQ: Enabling Verifiable Trajectory Range Queries in Hybrid-Storage Blockchains

Due to their increasingly large volumes, outsourcing of trajectory storage and querying to third-party service providers has become attractive. However, in such outsourced environments, service providers may return incorrect, e.g., incomplete, tampered, or invalid query results, making verifiability of query results an important consideration. Existing hybrid-storage blockchains offer limited support for trajectory data, lacking authenticated data structures (ADS) that enable efficient verification. For example, ADSs designed for queries on one-dimensional data are unsuitable for queries on multidimensional trajectory data, while ADSs tailored for discrete data may yield incomplete results when applied to continuous trajectory data. We propose the first framework for verifiable trajectory range queries in hybrid-storage blockchains, called VTRQ. It features two efficient ADSs: (i) a spatial ADS for road networks that leverages hierarchical organization to aggregate trajectory, edge, and node hashes, thus reducing redundant computations and improving spatial verification efficiency; and (ii) a temporal ADS based on interval trees, which indexes only the start and end times of trajectories, thereby enabling pruning and efficient temporal verification. By separating spatial and temporal indexing, the method reduces the need for data comparison, enhancing both query and verification efficiency. To aggregate spatial and temporal query results, VTRQ provides a spatio-temporal edge aggregation mechanism that combines temporal verification of spatial nodes, spatial intersection computation, and temporal intersection analysis to achieve spatio-temporal filtering.

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arXiv2026

Using Lower-Bound Representations for Trajectory Similarity Learning

Trajectory similarity learning is fundamental to efficient trajectory retrieval under complex distance measures. Existing learning-based methods typically rely on embeddings trained to approximate trajectory distances or rankings, but they often lack guarantees with respect to the original distances, exhibit unstable performance across distance measures, and incur substantial training costs. We revisit trajectory similarity learning from a lower-bound representation perspective and propose LB-TrajRep, a unified lower-bound representation framework independent of deep neural embeddings. This framework constructs single-vector representations from a set of lower-bound components, enabling admissible and interpretable lower bounds for multiple classical trajectory distances, including Dynamic Time Warping (DTW), Hausdorff distance, and Discrete Fréchet Distance (DFD). Within this framework, we instantiate point-pivot components, which naturally support both metric and non-metric distances and remain compatible with standard vector-based retrieval pipelines. To improve ranking quality, we develop two data-driven pivot selection strategies that explicitly optimize lower-bound tightness and prioritize hard near-neighbor trajectory pairs, respectively. Extensive experiments on real-world trajectory datasets show that the proposed lower-bound representations are able to consistently outperform state-of-the-art neural trajectory embeddings across diverse distance measures, improving top-$k$ ranking accuracy by up to 20\%--60\% on the Hausdorff distance and DFD and by 15\%--40\% on DTW.

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arXiv2026

SqLinear: Balanced Square Partitioning Makes Linear Interaction Sufficient for Large-Scale Traffic Forecasting

Traffic prediction is a core task in intelligent transportation systems and urban-scale decision making. Despite the effectiveness of mainstream neural network-based methods, their deployment in real-world settings with thousands of traffic sensors is severely jeopardized by their poor computational scalability. To address this, the community has attempted to incorporate spatial database partitioning techniques to improve model scalability. However, these approaches rely on handcrafted geometric heuristics and often produce irregular or imbalanced data partitions, leading to boundary fragmentation, excessive padding overheads, and degraded model accuracy. In this paper, we propose SqLinear, an efficient and effective architecture for large-scale traffic prediction. First, we design Square Partition, a geometry-adaptive algorithm that partitions massive traffic sensors into balanced, non-overlapping, and compact spatial regions. Unlike existing heuristic-based designs, Square Partition is theoretically grounded and provides provable guarantees on partition utilization and split balance, establishing a high-quality foundation for downstream spatio-temporal modeling. Next, we propose a Hierarchical Linear Interaction (HLI) module that abandons the costly attention mechanisms commonly used in Transformer-based spatio-temporal models. HLI efficiently propagates global inter-region dependencies and refines them at the node level through a lightweight linear interaction scheme, enabling effective spatio-temporal modeling with linear computational complexity. Extensive experiments on four large-scale traffic datasets and 11 baselines show that SqLinear reduces MAE by 2.30% on average under the standard setting and by up to 6.78% under extreme scalability settings, while reducing training runtime by 13.27%--30.84% in spatial- and horizon-scaling scenarios.

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arXiv2026

Impute On-Demand: Adaptive Correlated Time Series Imputation for Changing Environments

Internet of Things (IoT) applications generate vast amounts of Correlated Time Series (CTS) data that often contain missing values and require imputation. Existing methods emphasize accuracy but often lack adaptability to changing IoT environments: they are vulnerable to sensor failures, cannot selectively impute only incomplete sensors, and use static architectures that do not adapt to resource availability. To address these limitations, we propose AdaCTSi, an adaptive CTS imputer for changing environments. AdaCTSi combines a One-shot Temporal Convolutional Network with a Learned Time-Sensor Index Table to extract and decouple complex spatio-temporal features into sensor-wise embeddings, enabling adaptation to varying sensor subsets. Sparse Spatial Attention efficiently extracts dynamic spatial correlations, while Correlation-Weighted Sensor Selection selects informative sensors to provide sufficient spatial context. Experiments with twelve baseline methods, three adaptability scenarios, and five benchmark datasets covering traffic, air quality, and trajectory data show that AdaCTSi reduces MAE by an average of 33.1% relative to the strongest baseline on each dataset. A single trained model supports sensor-subset and resource-adaptive inference, and its modest memory footprint enables deployment on commodity computing devices, including MCUs.

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arXiv2026

PATRA: Pattern-Aware Alignment and Balanced Reasoning for Time Series Question Answering

Time series reasoning demands both the perception of complex dynamics and logical depth. However, existing LLM-based approaches exhibit two limitations: they often treat time series merely as text or images, failing to capture the patterns like trends and seasonalities needed to answer specific questions; and when trained on a mix of simple and complex tasks, simpler objectives often dominate the learning process, hindering the development of deep reasoning capabilities. To address these limitations, we propose the Pattern-Aware Alignment and Balanced Reasoning model (PATRA), introducing a pattern-aware mechanism that extracts trend and seasonality patterns from time series to achieve deep alignment. Furthermore, we design a task-aware balanced reward to harmonize learning across tasks of varying difficulty, incentivizing the generation of coherent Chains of Thought. Extensive experiments show that PATRA outperforms strong baselines across diverse Time Series Question Answering (TSQA) tasks, demonstrating superior cross-modal understanding and reasoning capability.

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arXiv2026

TimeBlocks: Foundational and Continual Time-Series Blockbase -- Extended Version

The ongoing digitization has led to a proliferation of time-series data streams that monitor a variety of processes, from which valuable insights may be obtained. Further, the emergence of successful foundational language models begs the question of whether it is possible to achieve time-series models with the foundational properties of handling multiple tasks, while being sufficiently lightweight to allow real-time data stream processing. Existing foundational time-series models are often large and only effective in offline settings without stringent time and computational constraints, and where repeated model calibration is not needed. However, when applied to data streams, these models are ineffective due to their size and lack of support for continual calibration, which compromise their ability to deliver accurate real-time responses, their durability, and their deployability in hardware-limited settings. We propose TimeBlocks to enable versatile time-series processing by facilitating the efficient building of lightweight models suitable for multiple tasks under variable conditions. In particular, the method maintains a pool of interchangeable and modular model blocks that can be used to construct new time-series models. When presented with specific time-series data, a routing strategy iteratively selects the most suitable blocks to construct a lightweight and accurate model for the data. We equip TimeBlocks with a method called StreamCore to build a representative small subset of the data stream, which preserves a guaranteed approximation of the stream over time, enabling continual model calibration. An experimental study on multiple data sets and covering multiple tasks shows that TimeBlocks enables to build models capable of outperforming existing baselines.

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arXiv2026

Reliable AI Needs to Externalize Implicit Knowledge: A Human-AI Collaboration Perspective

This position paper argues that reliable AI requires infrastructure for human validation of implicit knowledge. AI learns from both explicit knowledge (papers, documentation, structured databases) and implicit knowledge (reasoning patterns, debugging processes, intermediate steps). Implicit knowledge remains unexternalized because documentation cost exceeds perceived value -- yet AI learns from it indiscriminately, acquiring both beneficial patterns and harmful biases. Current reliability methods can only verify explicit knowledge against sources, creating a fundamental gap: the most valuable AI capabilities (reasoning, judgment, intuition) are precisely those we cannot verify. We propose Knowledge Objects (KOs) -- structured artifacts that externalize implicit knowledge into forms humans can inspect, verify, and endorse. KOs transform verification economics: what was previously too costly to verify becomes feasible, enabling accumulated human validation to improve reliability over time.

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arXiv2026

Automatic Unsupervised Ensemble Outlier Model Selection--Extended Version

Unsupervised outlier detection is attractive because it eliminates the need for labeled data. Moreover, forming multi-model ensembles can improve detection robustness. However, composing an ensemble without labeled data is challenging. Naively composed ensembles can suffer from ensemble saturation, where redundant or unreliable detection models degrade performance and incur unnecessary computation. We propose MetaEns, an automatic unsupervised framework for selecting ensembles of outlier detection models. Using labeled meta-datasets, MetaEns learns a model that predicts marginal ensemble gains, estimating the expected improvement from adding a candidate model to a partially constructed ensemble. At test time, this learned signal is combined with a submodular-inspired proxy objective that enforces diminishing returns through diversity-aware discounting and family-level risk regularization, thereby enabling greedy sequential selection with adaptive early stopping. As a result, MetaEns constructs compact, high-quality ensembles without access to ground-truth labels. Experiments on 39 real-world datasets show that MetaEns consistently outperforms state-of-the-art unsupervised selectors and ensemble baselines, achieving higher average precision while using fewer models.

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arXiv2026

Hermes: A Multi-Scale Spatial-Temporal Hypergraph Network for Stock Time Series Forecasting

Time series forecasting occurs in a range of financial applications providing essential decision-making support to investors, regulatory institutions, and analysts. Unlike multivariate time series from other domains, stock time series exhibit industry correlation. Exploiting this kind of correlation can improve forecasting accuracy. However, existing methods based on hypergraphs can only capture industry correlation relatively superficially. These methods face two key limitations: they do not fully consider inter-industry lead-lag interactions, and they do not model multi-scale information within and among industries. This study proposes the Hermes framework for stock time series forecasting that aims to improve the exploitation of industry correlation by addressing these limitations. The framework integrates moving aggregation and multi-scale fusion modules in a hypergraph network. Specifically, to more flexibly capture the lead-lag relationships among industries, Hermes proposes a hyperedge-based moving aggregation module. This module incorporates a sliding window and utilizes dynamic temporal aggregation operations to consider lead-lag dependencies among industries. Additionally, to effectively model multi-scale information, Hermes employs cross-scale, edge-to-edge message passing to integrate information from different scales while maintaining the consistency of each scale. Experimental results on multiple real-world stock datasets show that Hermes outperforms existing state-of-the-art methods.

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arXiv2026

Replacing Multi-Step Assembly of Data Preparation Pipelines with One-Step LLM Pipeline Generation for Table QA

Table Question Answering (TQA) aims to answer natural language questions over structured tables. Large Language Models (LLMs) enable promising solutions to this problem, with operator-centric solutions that generate table manipulation pipelines in a multi-step manner offering state-of-the-art performance. However, these solutions rely on multiple LLM calls, resulting in prohibitive latencies and computational costs. We propose Operation-R1, the first framework that trains lightweight LLMs (e.g., Qwen-4B/1.7B) via a novel variant of reinforcement learning with verifiable rewards to produce high-quality data-preparation pipelines for TQA in a single inference step. To train such an LLM, we first introduce a self-supervised rewarding mechanism to automatically obtain fine-grained pipeline-wise supervision signals for LLM training. We also propose variance-aware group resampling to mitigate training instability. To further enhance robustness of pipeline generation, we develop two complementary mechanisms: operation merge, which filters spurious operations through multi-candidate consensus, and adaptive rollback, which offers runtime protection against information loss in data transformation. Experiments on two benchmark datasets show that, with the same LLM backbone, Operation-R1 achieves average absolute accuracy gains of 8.83 and 4.44 percentage points over multi-step preparation baselines, with 79\% table compression and a 2.2$\times$ reduction in monetary cost.

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arXiv2026

DiSGMM: A Method for Time-varying Microscopic Weight Completion on Road Networks

Microscopic road-network weights represent fine-grained, time-varying traffic conditions obtained from individual vehicles. An example is travel speeds associated with road segments as vehicles traverse them. These weights support tasks including traffic microsimulation and vehicle routing with reliability guarantees. We study the problem of time-varying microscopic weight completion. During a time slot, the available weights typically cover only some road segments. Weight completion recovers distributions for the weights of every road segment at the current time slot. This problem involves two challenges: (i) contending with two layers of sparsity, where weights are missing at both the network layer (many road segments lack weights) and the segment layer (a segment may have insufficient weights to enable accurate distribution estimation); and (ii) achieving a weight distribution representation that is closed-form and can capture complex conditions flexibly, including heavy tails and multiple clusters. To address these challenges, we propose DiSGMM that combines sparsity-aware embeddings with spatiotemporal modeling to leverage sparse known weights alongside learned segment properties and long-range correlations for distribution estimation. DiSGMM represents distributions of microscopic weights as learnable Gaussian mixture models, providing closed-form distributions capable of capturing complex conditions flexibly. Experiments on two real-world datasets show that DiSGMM can outperform state-of-the-art methods.

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arXiv2026

CLEAR: A Knowledge-Centric Vessel Trajectory Analysis Platform

Vessel trajectory data from the Automatic Identification System (AIS) is used widely in maritime analytics. Yet, analysis is difficult for non-expert users due to the incompleteness and complexity of AIS data. We present CLEAR, a knowledge-centric vessel trajectory analysis platform that aims to overcome these barriers. By leveraging the reasoning and generative capabilities of Large Language Models (LLMs), CLEAR transforms raw AIS data into complete, interpretable, and easily explorable vessel trajectories through a Structured Data-derived Knowledge Graph (SD-KG). As part of the demo, participants can configure parameters to automatically download and process AIS data, observe how trajectories are completed and annotated, inspect both raw and imputed segments together with their SD-KG evidence, and interactively explore the SD-KG through a dedicated graph viewer, gaining an intuitive and transparent understanding of vessel movements.

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arXiv2026

VISTA: Knowledge-Driven Vessel Trajectory Imputation with Repair Provenance

Repairing incomplete trajectory data is essential for downstream spatio-temporal applications. Yet, existing repair methods focus solely on reconstruction without documenting the reasoning behind repair decisions, undermining trust in safety-critical applications where repaired trajectories affect operational decisions, such as in maritime anomaly detection and route planning. We introduce repair provenance - structured, queryable metadata that documents the full reasoning chain behind each repair - which transforms imputation from pure data recovery into a task that supports downstream decision-making. We propose VISTA (knowledge-driven interpretable vessel trajectory imputation), a framework that reliably equips repaired trajectories with repair provenance by grounding LLM reasoning in data-verified knowledge. Specifically, we formalize Structured Data-derived Knowledge (SDK), a knowledge model whose data-verifiable components can be validated against real data and used to anchor and constrain LLM-generated explanations. We organize SDK in a Structured Data-derived Knowledge Graph (SD-KG) and establish a data-knowledge-data loop for extraction, validation, and incremental maintenance over large-scale AIS data. A workflow management layer with parallel scheduling, fault tolerance, and redundancy control ensures consistent and efficient end-to-end processing. Experiments on two large-scale AIS datasets show that VISTA achieves state-of-the-art accuracy, improving over baselines by 5-91% and reducing inference time by 51-93%, while producing repair provenance, whose interpretability is further validated through a case study and an interactive demo system.

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arXiv2026

A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective

Multivariate Time Series Forecasting (MTSF) plays a crucial role across diverse fields, ranging from economic, energy, to traffic. In recent years, deep learning has demonstrated outstanding performance in MTSF tasks. In MTSF, modeling the correlations among different channels is critical, as leveraging information from other related channels can significantly improve the prediction accuracy of a specific channel. This study systematically reviews the channel modeling strategies for time series and proposes a taxonomy organized into three hierarchical levels: the strategy perspective, the mechanism perspective, and the characteristic perspective. On this basis, we provide a structured analysis of these methods and conduct an in-depth examination of the advantages and limitations of different channel strategies. Finally, we summarize and discuss some future research directions to provide useful research guidance. Moreover, we maintain an up-to-date Github repository (https://github.com/decisionintelligence/CS4TS) which includes all the papers discussed in the survey.

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arXiv2026

TimeART: Towards Agentic Time Series Reasoning via Tool-Augmentation

Time series data widely exist in real-world cyber-physical systems. Though analyzing and interpreting them contributes to significant values, e.g, disaster prediction and financial risk control, current workflows mainly rely on human data scientists, which requires significant labor costs and lacks automation. To tackle this, we introduce TimeART, a framework fusing the analytical capability of strong out-of-the-box tools and the reasoning capability of Large Language Models (LLMs), which serves as a fully agentic data scientist for Time Series Question Answering (TSQA). To teach the LLM-based Time Series Reasoning Models (TSRMs) strategic tool-use, we also collect a 100k expert trajectory corpus called TimeToolBench. To enhance TSRMs' generalization capability, we then devise a four-stage training strategy, which boosts TSRMs through learning from their own early experiences and self-reflections. Experimentally, we train an 8B TSRM on TimeToolBench and equip it with the TimeART framework, and it achieves consistent state-of-the-art performance on multiple TSQA tasks, which pioneers a novel approach towards agentic time series reasoning.

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