Multivariate Time-Series

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4 papers in the last four weeks, down 20% on the four weeks before. 0.0% of all new papers.

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Latest papers 62

Oct 1, 2026cs.CL

Scalable, Transferable Meta-network for Data Selection Requires a Different Loss (and Why the Obvious Choice is Problematic)

Data selection is critical for training large language models on massive and heterogeneous corpora. Meta-learning for Training-data Selection offers a principled alternative to heuristic scoring by learning data weights from a target validation objective, but existing methods face a trade-off between fine-grained valuation and transferability to unseen data. A natural solution is to replace per-sample weights with a selection network. However, we find that directly incorporating such a network into existing MTS objectives leads to unstable optimization and poor generalization, caused by weight suppression and persistent reliance on easy-to-learn features. To address these issues, we propose Transferable Example Scoring and Selection (TESS), a scalable data-selection framework built on a Pointwise Value Matching objective (PVM). Experiments on LLM safety and targeted instruction tuning demonstrate strong transfer across datasets, from subsets to full corpora, and from smaller to larger models.

Zilin Du, Bowen Yang, Boyang Albert Li

College of Computing and Data Science Nanyang Technological University Singapore

Natural Language Datasets Training Data Choice Multivariate Time-Series

Oct 1, 2026cs.AI

ProtoFlow: Prototype-Guided Flow Matching for Multivariate Time Series Forecasting

Generative modeling has shown strong promise for multivariate time mseries (MTS) forecasting, especially scale to high-dimensional settings. Diffusion-based methods achieve competitive performance but typically require many sampling steps at inference. VAE-based non-iterative forecasting frameworks have therefore emerged as an efficient alternative. Within this line of work, vector quantization (VQ) enables controllable latent space modeling by mapping multivariate series into compact discrete representations. Existing VQ-based forecasting methods, however, typically rely on autoregressive (AR) token generation, which suffers from exposure bias and training-inference mismatch. Flow matching provides an efficient non-autoregressive alternative for latent forecasting, but existing formulations usually initialize transport from a generic Gaussian prior. We instead observe that the trained VQ codebook already captures representative latent prototypes and can thus serve as a more informative prior for flow matching. Based on this insight, we propose ProtoFlow, a forecasting framework that combines vector-quantized autoencoding with Prototype-prior Flow matching. Our method first maps multivariate sequences into a discrete latent space, then constructs a structured prior from the learned codebook, and finally learns a DiT-based rectified flow to transport samples from this prior to future latent representations conditioned on historical observations. By replacing generic noise initialization with a learned prototype prior, ProtoFlow avoids the rollout mismatch of AR token prediction and promotes faster training convergence. Extensive experiments on benchmark datasets show that it consistently achieves superior forecasting performance with efficient inference.

Shibo Feng, Wanjin Feng, Yang Qiu +3

Nanyang Technological University · Tsinghua University · Shanghai Jiao Tong University

Multivariate Time Series Forecasting Vector-Quantized Variational Autoencoder Multivariate Time-Series Autoregressive Model Time Series

Sep 27, 2026cs.LG

Domain Generalization under Sampling Pattern Shifts in Irregular Time Series

Irregularly sampled multivariate time series (ISMTS) are prevalent in real-world applications, where both observation times and available measurements can vary substantially across domains. While recent models increasingly exploit such sampling information for prediction, its robustness under sampling pattern shifts remains underexplored. We introduce HAR-C, to the best of our knowledge the first controlled benchmark for sampling pattern shifts in ISMTS, and show that sampling shifts alone can substantially degrade performance, induce sampling-specific shortcuts, and remain challenging for existing domain generalization (DG) methods. Motivated by these findings, we propose PRISM, a DG framework that first learns complementary feature-centric and sampling-centric representations without task labels, and subsequently performs robust supervised training across diverse sampling variations to discourage brittle shortcut reliance. Extensive experiments on controlled and real-world ISMTS benchmarks demonstrate that PRISM consistently improves robustness to unseen sampling shifts over existing methods. Our code is available at https://anonymous.4open.science/r/PRISM.

Changhun Kim, Joohyung Lee, Kwanhyung Lee +3

University of Wisconsin–Madison · AITRICS · KAIST

Multivariate Time-Series Time Series Prism

Sep 21, 2026cs.LG

Spatiotemporal Kronecker Covariance Neural Networks

Multivariate time series contain complex patterns that span across both space and time. While covariance-based statistical tools like spatiotemporal Principal Component Analysis (ST-PCA) help identify these patterns, they are limited to linear operations and prone to estimation errors with limited data. Recent covariance-based spatiotemporal neural networks offer more stable, non-linear alternatives, but they ignore correlations across different time steps. To solve this, we introduce the Kronecker coVariance Neural Network (KVNN), a temporal graph neural network that represents the spatiotemporal covariance matrix via a sum of Kronecker products where spatial and temporal dependencies are decoupled. By implementing filtering operations on spatial and temporal components, KVNNs achieve expressive processing capabilities, admit a rigorous spectral analysis, and are provably stable to finite-sample estimation errors, ultimately addressing all of ST-PCA's limitations. We show on five real-world datasets that KVNNs achieve strong forecasting performance, often requiring significantly fewer trainable parameters than competitive methods, and are consistent under estimation noise.

Andrea Cavallo, Athanasios Georgoutsos, Elvin Isufi

Delft University of Technology, Delft, Netherlands

Spatio-Temporal Forecasting Spatiotemporal Multivariate Time-Series Covariance Neural Network

Sep 10, 2026cs.LG

RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation

Multivariate time series imputation (MTSI) aims to recover missing values in temporal data composed of multiple interdependent variables. This problem is central to real-world applications such as healthcare monitoring, traffic networks, and energy systems. Recent diffusion-based approaches have shown strong potential for probabilistic imputation by learning to generate missing values through iterative denoising. However, most existing approaches perform diffusion directly in the original data space, requiring the denoising network to simultaneously capture global structure, temporal dynamics, and stochastic variability. This makes the generative task unnecessarily complex, especially when modern deterministic imputers can already provide accurate initial reconstructions. To address this limitation, we propose RDDMPI, a conditional residual diffusion framework that operates directly in residual space. Instead of modeling the full missing signal directly, we reformulate probabilistic imputation as a baseline-residual decomposition, where a pretrained model captures the dominant signal and a diffusion process models the residual uncertainty. To better exploit deterministic guidance, \model{} conditions the reverse denoising process on both the baseline-completed signal and its latent representation, while a reliability-aware conditioning mechanism adaptively controls the influence of baseline information during residual generation. This formulation simplifies the diffusion learning objective, enabling it to focus on structured correction terms rather than reconstructing the full signal. Experiments on multiple benchmark datasets demonstrate that RDDMPI consistently improves both reconstruction accuracy and uncertainty quantification.

Ramiro Valdes Jara, David Chapman, Adam Meyers

Department of Industrial and Systems Engineering, University of Miami, United States of America · Department of Computer Science, University of Miami, United States of America

Imputation Residual Conditional Diffusion Model Multivariate Time-Series

Sep 3, 2026cs.LG

RATL: Learning from Retrieved Residuals for Robust Multivariate Time-Series Forecasting

Retrieval-augmented generation (RAG) complements parametric models with retrieved external evidence. The same idea is attractive for continuous-output regression, but directly reusing retrieved target values is often not robust when samples differ in output level, numerical scale, or local dynamics. Moreover, conventional forecasting pipelines generally use residuals for model optimization and error diagnosis, but do not retain individual historical residual examples as memory that can be accessed at inference time.For multivariate time-series forecasting, we propose RATL, a plug-in residual-retrieval and feedback-correction method. RATL freezes a base forecaster to construct retrieval keys and turns its historical forecast residuals into a train-only memory specific to that base model. At inference time, RATL retrieves residual trajectories from similar historical contexts subject to causal availability constraints, then uses a set-aware router operating over forecast blocks and variables to select and combine these trajectories. Experiments show that historical residuals matched to the current context contain reusable forecasting information and that RATL improves frozen base forecasters in most experimental settings. Ablations further show that learned routing strengthens raw residual feedback, while validation-based correction-strength selection limits residual over-injection.On real-world benchmarks, we use iTransformer as the primary frozen base forecaster, compare against multiple strong forecasting baselines, and test transferability across backbones. The results show that RATL can further improve base-forecaster performance in most settings.Overall, RATL shifts the retrieved object from historical target values to base-model-specific historical forecast errors, providing a plug-in, residual-memory-based paradigm for learned feedback correction in continuous-output forecasting.

Yuchen He, Yueyang Cang, Zhiyuan Ning +2

Department of Automation, Tsinghua University · State Key Laboratory of Hydroscience and Engineering, Tsinghua University

Residual Learning Multivariate Time-Series

Aug 12, 2026cs.LG

JAPE: Joint Anomaly Prediction and Intrinsic Explanation in Multivariate Time Series

Multivariate time-series anomaly prediction aims to identify whether and when anomalies will occur over a future horizon from historical observations. Existing methods primarily characterize anomalies as deviations in future numerical values, which may overlook subtle dependency changes induced by weak anomaly precursors and provide no native variable-level explanation together with the alert. To bridge these gaps, we propose JAPE, a Joint Anomaly Prediction and Explanation framework that lifts anomaly prediction from numerical-deviation modeling to dependency-structure modeling. JAPE is the first anomaly prediction framework to explicitly model evolving dependency structures for both point-wise alerting and native variable-level explanation. Specifically, JAPE (i) proposes a Decoupled Spatio-Temporal Representation (DSTR) backbone that decouples temporal and spatial modeling and captures lag-aware dependencies via learnable lag aggregation, thereby perceiving structural precursors before numerical deviations emerge; (ii) designs a dual-view alerting mechanism that fuses numerical forecasts with evolving dependency graphs for point-wise anomaly prediction, capturing structural evidence even under subtle numerical deviations; and (iii) presents Native Predictive Explanation (NPE), which directly reuses the predicted dependency graphs to rank variables by structural deviations without additional models or training. Extensive experiments on five real-world benchmarks across three prediction horizons demonstrate that JAPE improves average F1 and AUC-PR by 19.7% and 41.3%, respectively, while improving explainability with 26.6% gain in MRR.

Yian Wei, Yuanyuan Yao, Lu Chen +2

Zhejiang University · RMIT University · Aalborg University

Time-Series Anomaly Detection Interpretable Anomaly Detection Multivariate Time-Series

Aug 11, 2026cs.LG

GARLIC: Graph Attention-based Relational Learning of Multivariate Time Series in Intensive Care

Healthcare data, such as Intensive Care Unit (ICU) records, comprise heterogeneous multivariate time series sampled at irregular intervals with pervasive missingness. However, clinical applications demand predictive models that are both accurate and interpretable. We present our Graph Attention-based Relational Learning for Intensive Care (GARLIC) model, a novel neural network architecture that imputes missing data through a learnable exponential-decay encoder, captures inter-sensor dependencies via time-lagged summary graphs, and fuses global patterns with cross-dimensional sequential attention. All attention weights and graph edges are learned end-to-end to serve as built-in observation-, signal-, and edge-level explanations. To reconcile auxiliary reconstruction and primary classification objectives, we developed an alternating decoupled optimization scheme that stabilizes training. On three ICU benchmarks (PhysioNet 2012 & 2019, MIMIC-III), GARLIC sets the new state of the art in outcome prediction, significantly improving AUROC and AUPRC over best-performing baselines at comparable computational cost. Ablation studies confirm the contribution of each module, and feature-removal trials validate the fidelity of importance attribution through a monotonic performance drop (full > top 50% > random 50% > bottom 50%). Real-time case studies demonstrate actionable risk warnings with transparent explanations, marking a significant advance toward accurate, explainable deep learning for irregularly sampled ICU time series data. Moreover, we demonstrated \proposed{}'s superiority in data imputation and classification on various time-series datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks.

Ruirui Wang, Yanke Li, Manuel Günther +1

Department of Informatics University of Zürich · SCAI Lab, D-HEST ETH Zürich & SPF

Intensive Care Unit Multivariate Time-Series Missing Data Relational Deep Learning Relational

Aug 10, 2026cs.AI

An Explainable GNN Framework for Component-Level Anomaly Diagnosis

Industrial processes are complex systems composed of multiple interacting sensors that generate multivariate time series (MTS). Detecting anomalies in such systems is critical for reliability and safety, yet understanding their origin is equally important. Existing Graph Neural Network (GNN)based methods for anomaly detection primarily focus on sensor-level deviations and either attribute anomalies directly to the deviating sensors. When diagnosis is attempted, generally, the most deviated sensor is identified as a root cause of a system fault. However, in many industrial systems, anomalies do not arise from faulty sensors but from disruptions in the influences governing the system dynamics. We propose an explainable GNN-based anomaly detection framework that shifts the perspective from sensor-level anomalies to component-level diagnosis, hypothesizing that anomalous measurements are symptoms of altered inter-sensor influences. Experiments show that the method effectively identifies and prioritizes the true faulty components, providing interpretable insights into system failures.

Sena Ozgunay, Louise Trav{é}-Massuy{è}s, Jean-Michel Loubes +1

Comue de Toulouse, LAAS-DISCO, IMT · LAAS-CNRS, Université de Toulouse, France · Comue de Toulouse, LAAS-DISCO +4

Interpretable Anomaly Detection Graph Neural Networks Multivariate Time-Series Diagnosis

Aug 5, 2026cs.LG

Decoupling Perception from Description: Computation-Grounded Representation Alignment between Multivariate Time Series and Language

Training multimodal models to align time series with language runs into a self-supervision trap. The usual recipe asks an LLM to read a series and write a description, so label quality is capped by the perceptual skill the model is supposed to learn. The data can never teach more than the labeler already knows. A second gap makes this worse: most datasets use a single variable, but the patterns that matter (cross-channel correlation, lead-lag structure, co-occurring anomalies) appear only with several variables, right where the labeling LLM's limits are most exposed. These two problems create a trilemma: existing methods are reliable, realistic, or scalable, but none achieves all three. We resolve this by decoupling perception from description. Deterministic code computes a set of statistics from real, open-source multivariate series; the LLM verbalizes those precomputed facts. Perception, which LLMs do poorly, is handled by computation, while the LLM handles expression. This produces CGTime, our 4B-parameter computation-grounded time-series-language model. CGTime outperforms far larger general-purpose models on multivariate understanding tasks: it attains the best multivariate fact score on our held-out benchmark (0.283 vs. 0.173 for GPT-4o-mini and 0.203 for GPT-5.4-nano), a gap that survives Holm-corrected paired significance tests against every baseline. It also states verifiable numerical facts in generated captions more accurately and covers a broader range of statistical properties.

Xinran Feng, Yi Xie, Chao Zhang +4

Thrust of Financial Technology, The Hong Kong University of Science and Technology (Guangzhou) · Technical University of Munich · Heilbronn Data Science Center, Munich Data Science Institute +1

Multivariate Time-Series Automatic Labelling

Aug 3, 2026cs.LG

GLAIM: Learning Global and Local Adaptive Inter-Variable Dependency for Multivariate Time Series Imputation

Multivariate time series imputation is fundamental to downstream analysis, yet modeling inter-variable dependencies with incomplete observations remains challenging. Existing methods learn global dependencies across samples or dynamic local dependencies per sample. Global dependencies are stable but adapt poorly to sample variations and temporal non-stationarity, whereas local dependencies are adaptive yet unreliable when observations are insufficient, causing erroneous information propagation. To address these limitations, we propose GLAIM, a Global-Local Adaptive Inter-variable Dependency Modeling framework for multivariate time series imputation. GLAIM comprises two complementary components. The Stable Global Dependency Constructor derives robust global inter-variable dependencies from complementary temporal representations, providing a stable backbone less affected by sample-specific missingness and noise. The Sample-Conditioned Dependency Refiner adapts this backbone to each sample and time step using its temporal state and available observations, enabling reliable local refinement under incomplete observations. Extensive experiments on nine real-world datasets demonstrate that GLAIM achieves state-of-the-art performance under random and block missingness, remains robust to missing-rate shifts, and benefits from its complementary global and local components. Code is available at https://github.com/LuRenjias/GLAIM.

Mingyang Wang, Rongwen Li, Xiao Wang +1

College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China

Imputation Multivariate Time-Series Missing Data Non-Stationarity

Jul 31, 2026cs.LG

TFGformer: Multivariate Time Series Forecasting via Time-Frequency Graph Learning and Covariate Fusion

Large-scale multivariate time series from heterogeneous IoT sensors demand accurate long-term forecasting for resource scheduling and predictive maintenance. While recent time series foundation models exhibit strong generalization, they rely on static parametric knowledge and lack dynamic access to external historical patterns during inference. Retrieval-Augmented Generation (RAG) offers a potential remedy, yet its application to time series forecasting is challenged by magnitude variations across heterogeneous sources and the mismatch between historical similarity and future consistency. We propose CrossRAG, a retrieval-augmented forecasting framework that integrates Shape-Aware Memory (SAM) with RevIN normalization for magnitude-robust shape-level retrieval, Future-Consistent Contrastive (FCC) learning to distinguish informative references from hard negatives with similar history but divergent futures, and Cross-Attention Temporal Fusion (CATF) to fuse retrieved historical--future reference pairs into the backbone's representations at the representation level. Experiments on seven public benchmarks show that CrossRAG consistently outperforms both parametric-only baselines and existing retrieval-augmented forecasting methods.

Yu Sun, Yuan Chang, Xiaohou Shi +1

Beijing University of Posts and Telecommunications Beijing, China · China Telecom Research Institute Beijing, China

Multivariate Time Series Forecasting Retrieval-Augmented Forecasting Time Series Forecasting Multivariate Time-Series Multi-Stream Temporal Fusion Analogy

Jul 30, 2026cs.CL

Causal Discovery with Inverted Self-attention for Multivariate Time Series

Causal discovery in multivariate time series data is challenging due to complex interactions, high dimensionality, and nonlinear dependencies among variables. Existing methods often struggle to capture these complexities, resulting in inaccurate causal structures. To address this issue, we propose a novel framework that leverages self-attention mechanisms within the transformer architecture for causal discovery. Our approach introduces a novel inverted causal self-attention mechanism (CSAM) that emphasizes latent and indirect causal relationships by inverting tokens and inducing sparsity in attention scores, focusing on significant causal interactions and reducing spurious correlations. Additionally, we develop a global causal algorithm to identify global causal links, providing a holistic metric for causal influence, along with a causal verification module to ensure robustness in the identified causal relationships, enhancing the reliability of our framework. Experiments on both linear and nonlinear datasets, along with ablation studies and sensitivity analyses, show that our framework outperforms existing methods, demonstrating its potential for causal discovery in complex multivariate time series.

Yusen Liu, Yong Wang, Yifan Yin +3

School of Computer Science, University of Technology Sydney, Sydney, Australia · TianFu YongXing Laboratory, Chengdu, China · Faculty of Data Science, City University of Macau, Macau, China +1

Causal Discovery Methods Multivariate Time-Series Local Causal Structures Causal Attention

Jul 30, 2026cs.LG

Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework

Irregular multivariate time series are widely encountered in applications such as healthcare monitoring, human activity recognition, and environmental sensing. Their core challenges stem from asynchronous observations, non-uniform sampling intervals, and the fact that temporal patterns themselves carry critical dynamic information. Existing approaches either rely on discretization-based preprocessing (e.g., interpolation, imputation, or aggregation), which disrupts the underlying continuous-time semantics, or adopt continuous-time modeling via ODE-based frameworks, which typically require specialized architectures and incur substantial computational overhead due to numerical solvers. To address these limitations, we propose WrapFlow, a continuous-time modeling framework for irregular time series forecasting. On the input side, WrapFlow introduces Continuous-Time Tokenization, which directly encodes raw observation events and explicitly models long unobserved intervals via gap-aware tokens. The resulting continuous-time tokens are then processed by a standard Transformer backbone to capture long-range temporal dependencies. On the output side, we develop a simulation-free training paradigm for Residual Flow Matching, which learns conditional residual vector fields around base predictions while avoiding numerical-solver simulation and backpropagation during training. This design enables high-quality continuous forecasting using only a small number of fixed rollout steps at inference. Extensive experiments on multiple real-world datasets demonstrate that WrapFlow achieves state-of-the-art performance.

Tianen Shen, Zhengyu Li, Yutong Li +4

Multivariate Time-Series Time Series Vector Fields

Jul 25, 2026cs.LG

Domain-Prior-Regularized Graph Modeling for Anomaly Detection in Cyber-Physical Systems

Anomaly detection on multivariate sensor time series is critical for industrial monitoring of cyber-physical systems (CPS), where even subtle deviations from normal behavior can indicate process disruption. Recent graph-based approaches have made significant progress, but they often struggle in small-scale physical systems with scarce labeled anomalies and limited normal data. In such settings, graph-based models tend to capture spurious correlations and produce unstable sensor topologies. We propose DPR-GM (Domain-Prior-Regularized Graph Modeling), a forecasting-based framework that incorporates system design knowledge into graph construction. DPR-GM leverages a large language model (LLM) to extract directed physical couplings between sensor pairs from system documentation, which are encoded as a binary domain adjacency matrix serving as a structural gate over sensor relations. This gate is then modulated by Pearson correlations estimated from normal training data. The anomaly score is further weighted by sensor-level reliability derived from the coefficient of variation. All graph and weighting components are fixed prior to training and add no learnable parameters. On the SKAB benchmark, DPR-GM outperforms graph-based, statistical, and deep learning baselines across F1, AUROC, and AUPRC, showing that domain-structured graph priors are a practical alternative to fully learned topologies in data-scarce CPS.

Youngseok Hwang, Joonsung Kwon, Geonwoo Lee +1

Graduate School of Data Science, Seoul National University, Seoul, South Korea.

Generalist Graph Anomaly Detection Cyber-Physical System Anomaly Score Graph Representations Multivariate Time-Series

Jul 20, 2026cs.LG

Causal Discovery on Irregular Time Series

Causal discovery methods have shown strong performance in temporal systems, but they typically rely on regular and discrete lag structures, limiting their applicability to regularly sampled data. However, many real-world tasks require dealing with irregularly sampled streams of events, such as sensor streams, healthcare data, and financial transactions. In this work, we propose an extension of PCMCI+, a state-of-the-art method for causal discovery on regular multivariate time series, to allow for handling irregular time series. Instead of modelling causal relations through fixed-lag dependencies, our method aggregates causal influence over predefined temporal windows. We evaluate our method on synthetic irregular event streams with known causal structures under different signal-to-noise ratios, showing that it consistently recovers the underlying causal graph and substantially outperforms the standard PCMCI+ on irregularly sampled data.

Martim Penim, Ricardo Ribeiro Pereira, Jacopo Bono +3

1Feedzai, Portugal · 3DCC, Faculdade de Ciêncidas da Universidade do Porto, Portugal · 2Instituto Superior Técnico, Universidade de Lisboa, Portugal +1

Causal Discovery Methods Causal Graph Multivariate Time-Series Time Series

Jul 20, 2026cs.LG

TypiCore: A Hybrid Active Query Strategy for Class-Incremental Learning on Time Series

Time series data play a pivotal role across numerous domains, including healthcare and manufacturing. In real-world environments, models must cope with distribution shifts over time, a challenge commonly addressed through Continual Learning (CL) techniques. However, existing CL methods face a critical limitation: real-world data streams are rarely fully labeled, making annotation cost a major practical constraint. This paper investigates Active Class-Incremental Learning (ACIL) for multivariate time series, where a model must sequentially learn new classes while selectively querying labels under a fixed annotation budget. We present a systematic evaluation of a wide range of query strategies combined with multiple rehearsal-based approaches, assessing their impact on plasticity, stability, and label efficiency across four benchmark datasets. Our analysis reveals the limitations of uncertainty-based and distribution-aware methods in achieving strong performance under constrained labeling budgets. To address these shortcomings, we propose TypiCore, a novel hybrid query strategy that alternates between typicality-based and diversity-based sample selection across active learning cycles, enabling the construction of memory buffers that are both representative and diverse. Evaluated on the TSCIL benchmark, TypiCore delivers statistically significant improvements over all baselines and matches or surpasses fully supervised continual learning performance on multiple datasets while requiring a fraction of the available labels.

Gabor Szucs, Samuel Jacsev, Marcell Nemeth +2

Department of Telecommunications and Artificial Intelligence, Budapest University of Technology and Economics, Budapest, Hungary. · Department of Information Engineering, University of Padua, Padua, Italy.

Class-Incremental Learning Label Propagation Multivariate Time-Series Token Budget Allocation

Jul 18, 2026cs.LG

SurvCF(t): Counterfactual Explanations for Survival Analysis in Predictive Maintenance Multivariate Time Series Data

Predictive maintenance relies on accurate Remaining Useful Life estimation, often formulated using survival analysis over multivariate time-series data. While modern deep survival models achieve strong predictive performance, their black-box nature limits their use in safety-critical settings where actionable insight is required. In this work, we introduce \textit{SurvCF(t)}, the first framework for generating counterfactual explanations for survival models operating on time-series data. \textit{SurvCF(t)} identifies minimal, plausible, and temporally consistent changes to an asset's operational history that increase its predicted life time, framing explanation as a constrained optimization problem combining validity, proximity, sparsity, and plausibility. We evaluate the method on multiple benchmarks, including C-MAPSS, N-CMAPSS, and a real-world case study of the Scania Component_X dataset, demonstrating its ability to produce actionable and interpretable interventions. Our results show that \textit{SurvCF(t)} bridges the gap between survival prediction and prescriptive maintenance, enabling explainable and decision-oriented AI for maintenance strategies.

Zara Karazian, Panagiotis Papapetrou, Sindri Magnússon +2

Department of Computer and Systems Sciences (DSV) Stockholm University Stockholm, Sweden · Department of Electrical Engineering (ISY) Linköping University Linköping, Sweden

Counterfactual Explanation Survival Analysis Survival Predictions Predictive Maintenance Useful Life Prediction Multivariate Time-Series

Jul 18, 2026cs.LG

HyBDM: Multi-Scale Hybrid Experts for Time Series Forecasting with Bidirectional Dependency Modeling

Time series forecasting (TSF) is vital to many applications, yet existing models often struggle to capture the heterogeneous long-range global patterns and short-range local variations in multivariate time series. While some approaches partially model these dependencies, they often do not jointly exploit temporal and feature-wise information. To address this challenge, we propose HyBDM, a multi-scale hybrid model that decomposes temporal dynamics into global patterns and local variations, which are modeled by two specialized experts. The Global Patterns Expert employs an enhanced BiConv-Mamba module that integrates bidirectional convolutions, an M-SSM layer, a forgetting mechanism, and a GDD-MLP module for cross-channel modeling. The Local Variations Expert uses a Local Window Transformer (LWT) to perform efficient locality-aware attention with reduced computational complexity. In addition, a Multi-Scale Patcher and a Long-Short Router enable multi-resolution representations and adaptive fusion of the two experts. Experiments on six benchmark datasets show that HyBDM outperforms state-of-the-art methods in both forecasting accuracy and computational efficiency, demonstrating its effectiveness in bridging global-local dependencies for multivariate TSF.

Wenqiang Ma, Chen Cheng, Xue Cheng +1

Soul of Harlequin Lab

Multivariate Time Series Forecasting Multivariate Time-Series Time Series Forecasting Temporal Dynamics Mixture-Of-Experts Experts

Jul 15, 2026cs.LG

MIDiff: Tackling Sparsity and Imbalance in Mobile Usage Generation via Multivariate-Imaging Diffusion

Mobile usage traces are critical for tasks such as user behavior prediction and app recommendation, yet their use is constrained by privacy restrictions and costly large-scale data collection. Although generative models perform well on general time series, their application to mobile usage data remains challenging because (i) limited user activity causes severe sparsity, (ii) heterogeneous variable types complicate joint modeling, and (iii) functional differences across apps create pronounced usage imbalance. To address these challenges, we propose Multivariate-Imaging Diffusion (MIDiff), a diffusion-based framework operating in an imaging space defined by Cross-Gramian Angular Sum Field (C-GASF). C-GASF transforms sparse multivariate sequences into correlation images, while MIDiff employs Triple Attention in a U-Net to preserve temporal consistency and variable dependencies. Experiments show that MIDiff achieves state-of-the-art performance across fidelity metrics. In particular, it obtains a Discriminative Accuracy (DA) of 0.1526, compared with 0.3476 for the strongest baseline, ZITS-VAE, demonstrating its effectiveness in generating realistic and diverse mobile usage traces. Our code is available at https://github.com/YilaiLiu-HKU/MIDiff.

Yilai Liu, Shiyuan Zhang, Hongyang Du

Department of Electrical and Computer Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong SAR, China

Diffusion Models Generative Models Sparsity Multivariate Time-Series Class Imbalance

Jul 15, 2026cs.LG

VAIOM: Continuous-Input, Discrete-Output Decoder-Only Financial Sequence Modeling

Financial observations are continuous, heterogeneous, and noisy, whereas decoder-only next-token models are usually built around discrete symbolic inputs. We introduce Vector-Input Autoregressive Inference for Ordinal-Return Modeling (VAIOM), a decoder-only Transformer for probabilistic next-return modeling on one-hour foreign-exchange bars. VAIOM separates input representation from output likelihood: continuous multivariate financial-event vectors preserve numerical structure at the input, while a categorical distribution over the next volatility-normalized return bucket supports cross-entropy training and likelihood evaluation. The selected 0.9M Hybrid Continuous Input model combines continuous event features with categorical asset metadata, a Mixture-of-Market-States return head, Gap, volatility-regime, and Ordinal auxiliary objectives, and full-sequence supervision. Models and preprocessing are fit using pre-2024 Train data; models are selected on 2024H2 Validation and evaluated without refitting on two 2025 Test periods. Across three independent training seeds, every model outperforms fixed single-bar LightGBM baseline in both Test halves. For the canonical checkpoint, paired gains over LightGBM are 0.029 and 0.043 bits per event. Validation experiments show that continuous input improves over discrete-token input under the same categorical return objective, full-sequence supervision improves over last-position training, and auxiliary representation shaping together with a mixture-structured return head improves return likelihood in controlled comparisons. A supporting capacity study finds that the smallest evaluated complete architecture rung achieves the strongest Validation likelihood on the present corpus.

Yiming Ma, Xinyu Chen

Volatility Autoregressive Model Multivariate Time-Series

Jul 12, 2026cs.LG

Multi-Scale Convolution with Optimal Transport Attention Effect on Multivariate Time Series

The analysis of Multivariate Time Series (MTS) plays an important role in a lot of real-world practical applications, but it still remains some challenging problem about capturing multi-granularity structural patterns and suppressing noise appropriately. Multi-Scale Convolution with Optimal Transport Attention (MSC-OT) is proposed in this paper. MSC-OT is a useful architecture to optimize the attention mechanism. It combines multi-scale convolution with Sinkhorn optimal transport method based on inverted embedding. The inverted embedding approach embeds each variable as a token and allows the model to capture cross-variate relationships better. MSC-OT consists of two part: (1) Multi-Scale Convolution Enhancement, that applies multi-scale convolutions to attention score matrices based on inverted embedding, capturing local structural patterns in the variate-interaction space induced by compressed temporal representations; (2) Sinkhorn Optimal Transport Regularization, that formulates attention computation as an optimal transport problem and employs iterative matrix scaling to ensure balanced information flow across variates. Adaptive Fusion Strategy utilizes softmax-normalized learnable weights to dynamically combine base attention, convolution-enhanced, and OT-regularized scores. Experiments on widely-used datasets, including ETT, Electricity, Traffic, Solar-Energy, and Exchange-Rate, show that MSC-OT achieves well performance in both short-term and long-term forecasting tasks. Ablation experiments further validate the effectiveness of each proposed component and their synergistic contributions to improving prediction accuracy for multivariate time series forecasting.

HaoChong Fu, Jian Xu

Institute of Collaborative Innovation · University of Macau · Macau, China +2

Multivariate Time-Series Multi-Scale Convolution Impact Analysis

Jul 1, 2026cs.LG

Hierarchical Self-Supervised Representation Learning Framework for Multivariate Time Series Grounded in ECG Analysis

Data analysis in the medical domain often encounters scenarios involving a limited target dataset and a large, unannotated dataset with a general distribution. Under such circumstances, self-supervised learning (SSL) methods are highly effective for utilizing large datasets, making them a popular choice for electrocardiogram (ECG) analysis. This work presents the Event Reconstruction Joint-Embedding Predictive Architecture (ER-JEPA), a lightweight SSL framework for multivariate time series, whose name and two-fold hierarchical structure are inspired by the diagnostic approach of cardiologists. At its core, ER-JEPA features: (1) a two-stage structure that constructs representations for each time interval and subsequently processes these representations as a univariate time series, (2) the hierarchical integration of two Joint-Embedding Predictive Architectures (JEPAs), and (3) a Vision Transformer (ViT) backbone. The structural concatenation of two JEPAs categorizes the model as a Hierarchical JEPA (H-JEPA), designed to encode multiple levels of abstract representations for enhanced prediction on complex tasks. This study reports a successful application of H-JEPA to 12-lead ECG data as a multivariate time series, alongside an analysis of the sensitivity of hierarchical representation during the pretraining stage. Pretrained on approximately 180,000 10-second recordings, the model achieves state-of-the-art downstream performance on the ST-MEM benchmark, with rapid computation and minimal resource usage.

Siwon Kim

Research Institute of Basic Sciences, Seoul National University, Seoul, Korea

Video Joint Embedding Predictive Architecture Multivariate Time-Series Joint-Embedding Predictive Architectures Self-Supervised Learning S-Jepa

Jun 17, 2026cs.LG

Anomaly Detection for Sparse and Irregular Multivariate Time Series with Latent SDEs

Multivariate time series anomaly detection (MTSAD) is critical for a wide range of application areas, such as industrial monitoring, cybersecurity, or healthcare. Real-world data is often sparse, irregularly sampled or partially observed, yet existing methods assume uniformly sampled time series. We propose a generative approach based on Latent SDEs that projects the observed time series on a continuous-time stochastic dynamical system, directly being able to handle missing observations and irregular sampling, while also naturally capturing possible cyclic behavior that many real-world use cases inherently possess. Experiments on six anomaly benchmark datasets show that our proposed method ranks first among state-of-the-art baselines. We further demonstrate that our method remains robust under severe data sparsity, while performance significantly degrades for the tested baseline methods. These results highlight latent SDEs as a natural inductive bias for anomaly detection in multivariate time series, especially in presence of real-world irregularities.

Martin Uray, Dominik Geng, Florian Graf +2

Josef Ressel Centre for Intelligent and Secure Industrial Automation, University of Applied Sciences, Salzburg, Austria · University of Salzburg, Austria

Time-Series Anomaly Detection Multivariate Time-Series Time Series Stochastic Differential Equations Inductive Bias

Jun 15, 2026cs.LG

Phys-JEPA: Physics-Informed Latent World Models for Multivariate Time-Series Forecasting

Multivariate forecasting in physical systems requires models that predict coupled temporal variables while preserving meaningful state evolution. Deep forecasters can fit temporal correlations, and physics-informed models can regularize predictions with scientific constraints, but these directions are often connected only at the decoded-output level. As a result, the hidden predictive state that generates future trajectories may remain statistically useful but physically unstructured. We introduce Phys-JEPA, a physics-informed joint-embedding predictive architecture for multivariate time-series forecasting. Phys-JEPA learns a latent world model in which predictive states are decomposed into physical and residual components, and physical consistency is imposed directly on latent states and latent transitions rather than only on decoded forecasts. This formulation uses known physical variables to organize the representation space while retaining residual capacity for unresolved dynamics. On Jena Climate 2009--2016, Phys-JEPA reduces aggregate MSE from 0.12482 to 0.12273 and temperature MSE from 0.01892 to 0.01831 at H=24. On Traffic, full Phys-JEPA improves aggregate MSE over the supervised baseline across all tested horizons, reducing H=192 MSE from 0.800784 to 0.773873. On Electricity, the best variant depends on horizon: static latent consistency is strongest at H=24 and H=48, while full Phys-JEPA gives the best aggregate and target-variable MSE at H=192. These initial results suggest that moving physics-informed learning from output space to latent predictive state space is a promising direction for interpretable temporal world models.

Weizhi Nie, Weichao Liu, Honglin Guo +1

Tianjin University

Multivariate Time Series Forecasting Joint-Embedding Predictive Architectures Multivariate Time-Series Latent States Latent World Models S-Jepa

Jun 11, 2026cs.LG

A Stationarity-and-Coupling Criterion for Training-Free Time-Lagged Spectral Embeddings of Multivariate Time Series

We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is

D(τ)

, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contribution is not the descriptor but a falsifiable applicability criterion for it. Working from a stationary Gaussian VAR(1) model, we argue that

D(τ)

separates two classes when the signals are approximately stationary and the class information lives in their cross-channel temporal coupling rather than in marginal per-channel power. We derive, semi-formally, three consequences: a distinguishability condition, why the static (

τ=0

) covariance collapses to chance, and why a stationary but power-discriminated paradigm defeats the descriptor. The criterion is operational: a two-part pre-flight test -- an augmented Dickey-Fuller stationarity check and a power-baseline saturation check -- predicts applicability before any training. We validate both halves on a mixed assortment. On four paradigms that satisfy the criterion (Sleep-EDF, BCI-IV-2a, MIT-BIH, ESC-50) the descriptor is competitive with strong baselines at a fraction of their cost, reaching

88.5\pm4.5\%

under 20-subject leave-one-subject-out on Sleep-EDF on a single CPU thread. On three that violate it -- non-stationary ERPs, and financial-volatility and wearable-stress regimes that are power-discriminated -- it fails exactly as the pre-flight predicts, and these negatives are the more informative half. We are explicit that

D(τ)

is not the most accurate representation; its value is a compact, training-free embedding whose domain of validity is known in advance.

Siddharth Pal, Viktoria Rojkova

Multivariate Time-Series Stationarity Time-Frequency Full-Rank Correlation Matrices Timestep Embeddings Discriminative+1

Jun 11, 2026cs.LG

CRAFTIIF: Cross-Resolution Analytic Four-Type Interpretable Isolation Forest for Multivariate Time Series Anomaly Detection

Anomaly detection in multivariate time series is challenged by four structurally distinct anomaly types -- point (isolated spikes), distributional (level shifts), temporal (rhythm changes), and collective (inter-sensor correlation breakdowns) -- each requiring different feature representations. Most unsupervised methods target only one or two types and provide limited interpretability. We present CRAFTIIF (Cross-Resolution Analytic Four-Type Interpretable Isolation Forest), a fully unsupervised framework targeting all four types without dataset-specific tuning. CRAFTIIF generates K=500 random analytic wavelet feature draws across four families (Morlet, DOG, Haar, Coiflet), each targeting a specific anomaly type, feeding five structured Isolation Forests -- one per type plus a meta-IF for compound anomalies. An adaptive Otsu/MAD threshold calibrates detection automatically across anomaly rates from 0.1% to 69.2%. Because each IF is trained exclusively on type-specific features, branch firing provides direct anomaly-type attribution by construction, without post-hoc explanation. Evaluated on all 19 datasets of the mTSBench benchmark (Zhou et al., TMLR 2026), CRAFTIIF achieves mean F1=0.228 (all 19 datasets) and F1=0.322 (13 detectable datasets), ranking first among all 25 evaluated methods on VUS-PR (0.463 vs. previous best 0.329, +40.7%). A diagnostic framework -- oracle F1, detectability limits, and branch separation ratios -- identifies 6 of 19 datasets as fundamentally undetectable by any unsupervised method. Ablation over 11 conditions confirms adaptive thresholding (+38% F1), four-branch structure (+20%), and meta-IF (+23%) are each essential. Code: https://github.com/smitswil/craftiif

William Smits

Avathon, Austin, TX, USA

Time-Series Anomaly Detection Multivariate Time-Series Random Forest Wavelets

Jun 10, 2026cs.LG

Multi-Rate Mixture of Experts for Accelerating Liquid Neural Network Training

Multivariate time-series data often exhibit complex temporal dependencies, irregular sampling, and heterogeneous dynamics across multiple time scales, making accurate sequence modeling particularly challenging. Traditional recurrent neural networks (RNNs), such as Long Short-Term Memory (LSTM) networks, operate in discrete time and may struggle to effectively capture continuous and irregular temporal behaviors. Liquid Neural Networks (LNNs) address some of these limitations through continuous-time dynamics, but standard LNN architectures typically rely on a single dynamical system, limiting their ability to model heterogeneous temporal patterns. To address these challenges, we propose a Multi-Rate Mixture-of-Experts (MR-MoE) framework built on top of Liquid Neural Networks. In the proposed architecture, multiple LNN-based experts operate at distinct time scales, enabling the model to explicitly separate fast-changing dynamics from slow-evolving temporal trends. A gating network further enables adaptive expert specialization based on input conditions. In addition, we incorporate both feature-level and temporal attention mechanisms to improve robustness, interpretability, and long-range dependency modeling. Feature-level attention suppresses noisy or irrelevant variables, while temporal attention selectively focuses on informative historical states. We evaluate the proposed framework on a complex multivariate time-series prediction task and compare it against strong baselines, including LSTM, monolithic LNN, and standard MoE models. Experimental results demonstrate that the proposed MR-MoE framework consistently achieves improved AUROC and AUPRC performance while maintaining favorable computational efficiency. These results highlight the effectiveness of combining continuous-time dynamics, multi-scale expert decomposition, and adaptive attention mechanisms for time-series modeling.

Shilong Zong, Almuatazbellah Boker, Hoda Eldardiry

Department of Computer Science, Virginia Tech Blacksburg, VA 24061 USA · Department of Electrical and Computer Engineering, Virginia Tech Blacksburg, VA 24061 USA

Multivariate Time-Series Temporal Attention Timescale Neural Network Mixture-Of-Experts Experts

Jun 9, 2026cs.LG

LakeFM: Toward a Foundation Model for Aquatic Ecosystems Using Irregular Multivariate Multi-depth Time Series Data

Understanding and forecasting lake dynamics is critical for monitoring water quality and ecosystem health across lakes and reservoirs. While machine learning methods have been recently applied to ecological time-series data, existing works assume regular sampling in time and depth, and struggle to generalize across lakes with heterogeneous variables, depths, and observation patterns. To address these limitations, we introduce \textsc{LakeFM}, a foundation model for aquatic systems, pre-trained on large-scale ecological datasets comprising both simulated and observed lakes. Through extensive empirical evaluation, we show that \textsc{LakeFM} learns meaningful representations spanning broader lake-level characteristics, and achieves competitive or often superior-forecasting performance compared to existing time-series foundation and non-foundation models, while producing physically plausible predictions consistent with real-world lake dynamics.

Abhilash Neog, Sepideh Fatemi, Medha Sawhney +9

Virginia Tech Blacksburg, VA, USA · Grand Valley State University Muskegon, MI, USA · University of Wisconsin - Madison Madison, WI, USA +2

Time Series Foundation Models Multivariate Time-Series Coral Foundation Model

Jun 8, 2026cs.LG

Structured Adaptive Tensor Prediction for Streaming Data

Matrix-valued time series arise in a wide range of applications, such as spatio-temporal data from medical imaging and geophysics. Existing methods are mainly designed for static settings and lack adaptability to streaming and time-varying environments. Adaptive filtering techniques have also been largely limited to data with scalar or vector values, leaving adaptive forecasting for matrix-valued time series inadequately understood. To bridge these gaps, we develop an adaptive tensor regression framework that includes Matrix-on-Matrix (MoM) and Tensor-on-Matrix (ToM) formulations for streaming matrix-valued prediction. The two formulations differ in whether to directly model matrix-valued outputs or to exploit temporal structure via higher-order tensor representations. For the proposed tensor regression framework, we develop stochastic gradient descent (SGD) algorithms for online learning. We show that stacking multiple responses across time into higher-order tensors improves performance; in particular, the ToM achieves lower steady-state error and stronger denoising capability than MoM, motivating our focus on the ToM model. We further characterize the tracking behavior of SGD under time-varying dynamics. From a statistical perspective, we establish fixed-time recovery guarantees for ToM under general low-dimensional structures, including sparsity, low-rankness, and their joint sparselow-rank models.

Zhen Qin, Yang Chen

Michigan Institute for Computational Discovery and Engineering, Department of Statistics, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA · Department of Statistics, University of Michigan, Ann Arbor, MI 48109 USA

Multivariate Time-Series Autoregressive Model Streaming

Jun 4, 2026cs.LG

PAMF: Prior-Aware Multimodal Fusion for Incomplete Time Series Data

In healthcare, multimodal time series tasks often operate on incomplete observations in practice, for example when ECG segments are lost because electrodes detach or an entire respiratory channel is unavailable during overnight monitoring. Such missingness typically appears in two structurally distinct patterns: within-modality missing, where values are absent within an otherwise observed modality, and modality-level missing, where an entire modality is unavailable. Existing methods typically represent unobserved data implicitly through masks or missing embeddings, without learning instance-specific missing information, and most are designed for only one missingness pattern. A natural approach is to explicitly estimate the missing data; however, existing imputation methods treat missingness uniformly despite their different structural priors, and the imputation process is often isolated from downstream tasks, preventing downstream tasks from guiding imputation toward more informative representations. To address these limitations, we present PAMF, a multimodal time-series framework that explicitly handles different missingness patterns while coupling imputation with downstream prediction through prior-aware flow matching and weight sharing. Specifically, the method initializes the flow-matching source state with type-specific priors to distinguish two missing types. It further connects imputation and classification through architecturally matched encoders with weight sharing, transferring task-relevant representations into the imputation process. Experiments on multiple multimodal healthcare time-series benchmarks show that the proposed method achieves the strongest overall downstream performance across diverse datasets and missing settings compared with existing baselines.

Ziwen Kan, Wugeng Zheng, Tianlong Chen +1

Department of Computer Science, University of Central Florida · Department of Computer Science, University of North Carolina at Chapel Hill

Imputation Missing Modalities Multivariate Time-Series Multimodal Fusion Time Series Prior Knowledge Integration

Jun 2, 2026stat.ML

Combining Statistical Features and Deep Encodings for Rehearsal-Based Class-Incremental Time Series Classification

Many systems used in real-world environments require adding new categories and incorporating new information without forgetting what was previously learnt by the classification model. This is known as class-incremental continual learning, and in the case of multivariate time-series, is further complicated by the temporal structure of the data. In this paper, we present a novel approach for performing class incremental continual learning for the classification of multivariate time series data based upon the construction of a dual-stream feature extraction pipeline (using both deep temporal embedding features generated via a pre-trained frozen foundation model and application of statistical features). Evaluated on five benchmark datasets, the proposed system achieves competitive average accuracy across all datasets while maintaining low forgetting rates across all experimental configurations.

Pablo García-Santaclara, Bruno Fernández-Castro, Rebeca Pilar Díaz-Redondo

atlanTTic – ICLAB, Universidade de Vigo, Vigo 36310, Spain · Centro Tecnolóxico de Telecomunicacións de Galicia (GRADIANT), Vigo 36214, Spain

Time-Series Classification Class-Incremental Learning Multivariate Time-Series Timestep Embeddings

Jun 1, 2026cs.LG

Anomalies in Multivariate Time Series Benchmarks Are Mostly Univariate

Many recent multivariate time series anomaly detection (MTSAD) models incorporate cross-channel modeling, under the implicit assumption that the structure of anomalies may be spread across multiple channels. We evaluate this assumption on eight widely used public benchmarks by introducing a per-segment diagnostic framework that flags, for each labeled anomaly, whether at least one channel deviates individually from its normal history, whether the cross-channel correlation structure changes, or both. The framework shows that no cross-channel rupture occurs without an accompanying univariate deviation across a range of reasonable thresholds. A complementary metric also reveals that on six of the eight benchmarks, at least half of the labeled anomaly segments deviate univariately on 89% to 100% of their timesteps, reaching 100% on three of these datasets. To verify that our framework captures cross-channel structure when present, we construct synthetic data of phase-shifted sinusoidal channels with shared noise. Each anomalous segment is altered through one of two channel-wise corruptions that preserve the per-channel marginal distribution while breaking cross-channel structure, and our framework correctly characterizes these segments as cross-channel-only. On these data, channel-dependent (CD) models successfully exploit the cross-channel signal whereas channel-independent (CI) ones fail. The CI/CD comparison of a recent SOTA detector on real benchmarks further confirms that CD modeling brings no measurable gain. We conclude that current MTSAD benchmarks are unsuitable for validating cross-channel modeling capabilities, and we call for the development of more structurally diverse evaluation sets. The code for this study is publicly available.

Marc Pinet, Julien Cumin, Samuel Berlemont +1

Orange Research, Meylan, France · Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble, France

Time-Series Anomaly Detection Multivariate Time-Series Time Series Diagnostic Framework

May 27, 2026cs.LG

QuITE: Query-Based Irregular Time Series Embedding

Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven Multivariate Time Series (MTS) models, or (ii) map IMTS onto regular temporal grids through interpolation, which may distort temporal dynamics by introducing artificial values. To address these limitations, we propose a new input-embedding-based approach. We identify that the key bottleneck lies not in the backbone architecture, but in conventional embedding layers that assume uniform sampling. In this work, we introduce QuITE (Query-Based Irregular Time Series Embedding), a simple yet effective plug-and-play embedding module for IMTS. QuITE employs learnable query tokens to aggregate irregular observations through a single self-attention layer, directly producing backbone-compatible latent representations without artificial value generation or architectural modification. Extensive experiments on real-world benchmarks show that QuITE consistently improves MTS models, yielding average relative gains of up to

54.7\%

in forecasting and

15.8\%

in classification across diverse datasets and backbone architectures. Code is available at: https://github.com/Meaningfull9502/QuITE.

Junghoon Lim

SK Shieldus, Seongnam, Republic of Korea

Timestep Embeddings Multivariate Time-Series Time Series Temporal Dynamics Future Latent Representations

May 27, 2026cs.LG

Benchmarking Inductive Biases for Multivariate Time-Series Anomaly Detection with a Robust Multi-View Channel-Graph Detector

We present a unified experiment, analysis, and benchmark study of multivariate time-series (MTS) anomaly detection. Ten family-representative detectors -- spanning statistical, reconstruction, association, frequency, and generic-transformer families -- are evaluated on five datasets (SMD, MSL, SMAP, PSM, and MSDS) under effectiveness, efficiency, robustness, and cross-dataset generalisation. All methods share the same windowing, scoring, hardware, and metric protocols. Effectiveness, ablation, and robustness use three random seeds; cross-dataset transfer uses seed~0 because each extra seed requires

250

source-target evaluations. The benchmark yields three method-independent findings: no single-bias baseline dominates; absolute perturbation VUS-ROC is more informative than retention ratios; and MSDS behaves as an event-dense deployment workload rather than a sparse point-anomaly benchmark. Under this protocol we also introduce \ours{}, an adaptive detector family combining a NOTEARS-constrained directed channel-graph view with optional patch-attention and temporal-association views. \ours{} achieves the best macro-average VUS-ROC (

0.675

,

+5.1

~pt over the second-best LSTM-AE), ranks first overall, and reaches the top-3 on all five datasets. Its wins on MSL and MSDS are narrow, while its average and robustness gains are larger: under the same three-seed robustness protocol for every method, it obtains the strongest absolute VUS-ROC across noise, channel dropout, and time-shift perturbations. We release the MSDS preprocessing protocol, configurations, scripts, and seed-level metric dumps.

Junhao Wei, Yanxiao Li, Bidong Chen +9

Faculty of Applied Sciences, Macao Polytechnic University, Macao SAR, China · 2Macao Polytechnic University, Macao SAR, China

Time-Series Anomaly Detection Multivariate Time-Series Roc-Auc Multi-View Cnn-Lstm Inductive Bias

May 22, 2026cs.LG

Contrast to Detect: Dynamic Graph Contrastive Regularization for Unsupervised Anomaly Detection in Multivariate Time Series

Anomaly detection in multivariate time series (MTS) is hindered by dynamic inter-variable dependencies and feature entanglement under spectral noise, and in practice, is further complicated by the absence of anomaly labels. Existing reconstruction-based detectors tend to recover anomalies as faithfully as normal patterns, while prevailing graph contrastive methods enforce invariance across views and thus assume a stationary relational structure, an assumption that breaks under structural drift in real systems. We propose ContrastAD, an unsupervised framework that turns structural evolution itself into a learning signal rather than suppressing it. A Multi-Perspective Embedder encodes inputs from temporal, attribute, and structural perspectives. A Frequency-Aware Attention Mixer then performs spectral top-K filtering before attention, preventing noise from leaking into query-key similarities. The core component, a Dynamic Graph Contrastive Learner, builds power-law-inspired sparse graph snapshots from batch-level DTW distances and contrasts the most divergent pair against a stable anchor, regularizing the latent space without imposing rigid invariance. Across five real-world benchmarks, ContrastAD attains the highest mean F1 on all five datasets and the highest AUC on three (SWaT 93.60, SMD 98.66, PSM 97.79), with statistically significant F1 and AUC margins over the strongest baseline on SWaT and PSM. On MSL and SMAP, it trails the AUC leader by under 0.7 points while still leading on F1. Ablation and sensitivity studies further confirm that the contrastive objective works best as a soft regularizer, supporting our claim that strict invariance is suboptimal under non-stationary dynamics.

Yunhua Pei, Zixing Song, Jin Zheng +1

School of Computer Science, University of Bristol, Bristol, UK · School of Engineering Mathematics, University of Bristol, Bristol, UK

Time-Series Anomaly Detection Graph Anomaly Detection Multivariate Time-Series Contrastive Learning Spectral Filtering Multimodal Embeddings+1

May 22, 2026cs.LG

Valid and Expressive Copulas for Irregular Multivariate Time Series

We introduce CopFITi, a copula model for probabilistic forecasting of irregular multivariate time series (IMTS). Our model combines the expressivity of normalizing flows for univariate marginals with the consistency and flexibility of a Gaussian Mixture Copula for the joint dependency structure. Our experiments show that copula-based approaches, which decouple the marginals from the joint, yield better marginal models than architectures that directly fit the full joint. With CopFITi, we propose the first IMTS copula that is marginalization-consistent by construction and establish a new state of the art in joint IMTS density modeling.

Christian Klötergens, Tom Hanika, Lars Schmidt-Thieme +1

Institute of Computer Science University of Hildesheim Hildesheim, Germany

Gaussian Copula Multivariate Time-Series Probabilistic Forecasting Validation

May 22, 2026cs.LG

VACE: Learning Geometrically Structured Representations for Time Series Anomaly Detection

Anomaly detection in multivariate time series is a critical task across a wide range of real-world applications, where abnormal behaviour is rare, labels are unavailable, and the cost of a miss is high. The central challenge is learning a characterisation of normality precise enough to flag deviations. Representation self-supervised learning, typically through contrastive approaches, addresses this by embedding temporal patches into a latent space where normality occupies a well-defined region, with anomalies detected by geometric deviation. However, contrastive approaches shape this space indirectly through pair-sampling heuristics, providing no explicit control over the geometric structure that distance-based scoring requires. This means how tightly normal representations are grouped, and whether distances are directionally meaningful. We present VACE (Velocity-Aligned Channel Embeddings), a self-supervised anomaly detection method that represents normality as a compact, directionally coherent region in the embedding space. To this end, VACE trains a channel-aware encoder through a velocity-consistency objective, with no negatives and no synthetic anomalies, so that normal trajectories are locally smooth and aligned. At test time, a Mahalanobis positional score and a velocity-bank directional score are combined multiplicatively, flagging points that are simultaneously off-distribution and dynamically atypical. Despite its simplicity, VACE achieves state-of-the-art performance on TSB-AD-M under rigorous evaluation, significantly outperforming more complex methods trained on substantially larger budgets.

Alberto D. Cencillo, Leonardo Concepción, Isaac Triguero +1

1Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI) · Department of Computer Science and Artificial Intelligence (DECSAI), University of Granada, Granada, 18071, Spain

Time-Series Anomaly Detection Multivariate Time-Series

May 22, 2026cs.LG

Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack flexibility, whereas deep generative models struggle to capture complex temporal dependencies without extensive data and computation. We introduce Parametric Prior Mapping (PPM), a framework that injects parametric structural priors into a generative modeling process. Specifically, PPM utilizes a parametric estimator to derive a dynamic, adaptive prior that guides the learning of a complex predictive distribution via a learnable mapping. This design allows the model to retain the efficiency of parametric methods while exploiting the expressive power of generative models. Trained with a hybrid objective, PPM yields precise forecasts with well-calibrated uncertainty estimates. Empirical results show that PPM outperforms existing baselines in handling non-stationary data, offering a superior trade-off between accuracy and computational efficiency. The code is available at https://github.com/ljl8336/PPM.

Jinglin Li, Jun Tan, QI Fang +1

School of Computer Science and Engineering, Central South University, Changsha, China.

Probabilistic Forecasting Multivariate Time-Series Non-Stationarity Generative Models

May 21, 2026cs.CE

Dynamic Hypergraph Representation Learning for Multivariate Time Series without Prior Knowledge

Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex systems. However, a key challenge is the derivation of hypergraph representations from time series data in situations where the structure of the hypergraph is limited or absent. In this study, we propose a model that constructs a dynamic hypergraph representation for multivariate time series without relying on prior knowledge of the data. This is achieved by applying community detection to the time series and transforming the resulting communities, obtained through an attention mechanism, into a hypergraph using a clique-based technique. Hypergraph representations are derived from different time series datasets, and the resulting hypergraphs are then used by a Dynamic Hypergraph Attention Convolution Network (DHACN) for multivariate time series predictions. This research advances the field of hypergraph representation by introducing a novel approach that is better suited to uncover high-order relationships without prior knowledge.

Marco Gregnanin, Johannes De Smedt, Giorgio Gnecco +1

IMT School for Advanced Studies Lucca · KU Leuven · University of Chieti-Pescara

Multivariate Time-Series Hypergraphs Temporal Graph Neural Networks Community Detection Graph Neural Networks

May 21, 2026cs.LG

Prototype-Guided Classification Sub-Task Decoupling Framework: Enhancing Generalization and Interpretability for Multivariate Time Series

Time Series Classification (TSC) is a long-standing research problem that has gained increasing attention in recent years with the rapid growth of large-scale temporal data. Despite substantial progress enabled by deep learning, designing TSC models that are both accurate and interpretable remains a challenging task. Many existing approaches adopt a direct feature-to-label classification paradigm, by collapsing high-dimensional temporal embeddings into class logits via a single linear projection (often after global pooling), the paradigm conflates feature extraction and decision logic into an inseparable mapping. To address these limitations, we propose PDFTime, a prototype-guided framework that reformulates time series classification as a multi-stage decision process. Instead of direct feature-to-label mapping, PDFTime leverages learned prototypes to approximate class-conditional feature distributions in the latent space, enabling progressive discrimination through classification sub-tasks of varying granularity. To our knowledge, PDFTime is the first framework to reformulate time series classification as a decoupled, multi-stage similarity-based reasoning process, breaking the long-standing paradigm of direct, black-box feature-to-label mapping. Extensive evaluations demonstrate that PDFTime achieves state-of-the-art (SOTA) performance across UEA and UCR benchmarks. Notably, it secures the top-

1

accuracy on 80 out of 128 datasets in the UCR archive, significantly outperforming recent strong baselines in both consistency and generalization.

Xianhao Song, Yuang Zhang, Yuqi She +2

East China Normal University · Shanghai Jiao Tong University

Time-Series Classification Multivariate Time-Series Time Series Timestep Embeddings Interpretability

May 21, 2026cs.LG

CASE-NET: Deep Spatio-Temporal Representation Learning via Causal Attention and Channel Recalibration for Multivariate Time Series Classification

Multivariate time series (MTS) classification is foundational to pervasive computing and financial analysis, yet existing multi-scale paradigms are often constrained by suboptimal representation fidelity. We identify two critical bottlenecks: temporal non-causality in standard encoders that induces temporal confounding in non-stationary dynamics, and the absence of explicit channel saliency mechanisms that allows noise to contaminate the latent space. To address these challenges, we propose the Causal Attention and Spatio-temporal Encoder Network (CASE-NET), an architecture designed for structural manifold pre-conditioning. CASE-NET synergizes a Causal Temporal Encoder, which enforces physical arrow-of-time constraints via masked self-attention and causal convolutions, with an Adaptive Channel Recalibration module functioning as an information bottleneck to suppress detrimental noise. Comprehensive evaluations across six heterogeneous domains demonstrate that CASE-NET establishes new state-of-the-art benchmarks on four tasks, achieving a peak accuracy of 98.6% on the AWR dataset and superior robustness in non-stationary regimes.

Fan Zhang, Yating Cui, Hua Wang

Shandong Technology and Business University · Ludong University

Time-Series Classification Multivariate Time-Series Spatiotemporal Representations Spatial Encoding Causal Attention Information Bottleneck+1

May 21, 2026stat.ME

Causal Discovery in Structural VAR Models Under Equal Noise Variance

Causal discovery from multivariate time series is challenging when causal effects may occur both across time and within the same sampling interval. This issue is especially important in applications such as neuroscience, where the sampling rate may be coarse relative to the underlying dynamics and contemporaneous effects need not form an acyclic graph. We study causal discovery in linear Gaussian structural VAR models under an equal noise variance assumption, meaning that the structural noise terms have a common variance. Unlike the DAG-based cross-sectional equal noise variance setting, the time-series setting considered here does not generally yield point identification of a unique causal graph. Instead, multiple structural VAR parameterizations can induce the same stationary observed process law. We introduce a notion of observational equivalence tailored to this setting and show that the corresponding equivalence class is characterized by orthogonal transformations of the structural equations together with a global positive scale. This characterization leads to an equivalence-aware model discrepancy, the observational alignment discrepancy, which compares structural models modulo transformations that preserve the observed law. Building on this theory, we propose ENVAR, a sparsity-based procedure that searches over the induced observational equivalence class for a sparse normalized structural representative. We evaluate the proposed methodology on synthetic structural VAR data and on an fMRI dataset.

SeyedSina Seyedi HasanAbadi, Fahimeh Arab, Erfan Nozari +1

Bourns College of Engineering, University of California, Riverside · University of California, San Francisco · Department of Mathematics and Statistics, Boston University

Multivariate Time-Series Equivalence Visual Autoregressive Models

May 19, 2026cs.LG

Latent Laplace Diffusion for Irregular Multivariate Time Series

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Zinuo You, Jin Zheng, John Cartlidge

School of Computer Science, University of Bristol · School of Engineering Mathematics and Technology, University of Bristol

Long-Horizon Forecasting Multivariate Time-Series Generative Models

May 18, 2026cs.LG

XCTFormer: Leveraging Cross-Channel and Cross-Time Dependencies for Enhanced Time-Series Analysis

Multivariate time-series analysis involves extracting informative representations from sequences of multiple interdependent variables, supporting tasks such as forecasting, imputation, and anomaly detection. In real-world scenarios, these variables are typically collected from a shared context or underlying phenomenon, suggesting the presence of latent dependencies across time and channels that can be leveraged to improve performance. However, recent findings show that channel-independent (CI) models, which assume no inter-variable dependencies, often outperform channel-dependent (CD) models that explicitly model such relationships. This surprising result indicates that current CD models may not fully exploit their potential due to limitations in how dependencies are captured. Recent studies have revisited channel dependence modeling with various approaches; however, these methods often employ indirect modeling strategies, which can lead to meaningful dependencies being overlooked. To address this issue, we introduce XCTFormer, a transformer-based channel-dependent (CD) model that explicitly captures cross-temporal and cross-channel dependencies via an enhanced attention mechanism. The model operates in a token-to-token fashion, modeling pairwise dependencies between every pair of tokens across time and channels. The architecture comprises (i) a data processing module, (ii) a novel Cross-Relational Attention Block (CRAB) that increases capacity and expressiveness, and (iii) an optional Dependency Compression Plugin (DeCoP) that improves scalability. Through extensive experiments on three time-series benchmarks, we show that XCTFormer achieves strong results compared to widely recognized baselines; in particular, it attains state-of-the-art performance on the imputation task, outperforming the second-best method by an average of 20.8% in MSE and 15.3% in MAE.

Israel Zexer, Omri Azencot

The Stein Faculty of Computer and Information Science Ben-Gurion University of the Negev

Multivariate Time-Series Temporal Dependence Time Series Cross-Attention Latent Variable

May 18, 2026cs.LG

L-Drive: Beyond a Single Mapping-Latent Context Drives Time Series Forecasting

Mainstream methods for multivariate time-series forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing forecasting reliability. To address this issue, we propose L-Drive, a change-aware forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between forecasting accuracy and computational efficiency.

Fan Zhang, Shijun Chen, Hua Wang

Shandong Technology and Business University, Yantai, Shandong, China · Ludong University, Yantai, Shandong, China

Time Series Forecasting Multivariate Time-Series Time Series Autonomous Hard Drive Disassembly Absolute Pose

May 17, 2026q-fin.CP

Enhancing Regime Shift Detection Using Unstructured Data: A Study on the Treasury Market

Regime shifts in financial markets reorganise the joint dynamics of asset prices and macro variables, breaking any single-regime calibration. They are nonetheless difficult to detect reliably because the data signal is noisy and heavily multicollinear, while the contemporaneous text that announces them is unstructured. Standard regime shift detection methods rely solely on structured time-series data and ignore policy communications, even though these texts often signal shifts before they materialise in observed prices. We propose a text-enhanced regime shift detection pipeline that combines large language model (LLM) reasoning over central-bank communications with statistical validation on multivariate financial time series. The framework is detector-agnostic: text-proposed candidates are validated using a bootstrap likelihood-ratio test on a vector autoregression (VAR), while data-driven candidates from arbitrary regime detectors are ratified through a lenient LLM text check. We evaluate the framework on 2010-2024 FOMC minutes paired with a 14-variable U.S. Treasury and macroeconomic panel, using four interchangeable data-driven detectors. The proposed pipeline achieves F1 = 0.82 against a verified anchor list of monetary-policy regime shifts, with same-day modal detection latency and consistently stronger performance than pure data-driven baselines. The results demonstrate that combining unstructured policy text with statistical structural-break detection improves the robustness and interpretability of regime shift identification in financial markets.

Mingxuan Yi, Vidal Mehra, Jing Chen +1

School of Engineering Mathematics and Technology, University of Bristol, UK · Propellant Digital B.V., Amsterdam, Netherlands · School of Mathematics, Cardiff University, UK

Financial Sentiment Analysis Unstructured Data Multivariate Time-Series

May 16, 2026stat.ML

CAST: Causal Anchored Simplex Transport for Distribution-Valued Time Series

Many decision-facing stochastic systems are observed through aggregate distributions rather than scalar trajectories: queue occupancies, mobility shares, public-health mixtures, generation-source shares, ecological compositions, and air-quality severity profiles all live on the probability simplex and evolve over time. We study causal (online) forecasting for these distribution-valued time series and argue that the transition operator itself should be structured around the simplex. We introduce CAST (Causal Anchored Simplex Transport), a successor-local operator that (i) retrieves empirical successors from causal context, (ii) stabilizes them with a persistence anchor, and (iii) applies a bounded local stochastic transport on ordered supports; every stage preserves the simplex by construction. We identify a structural failure mode, latent transition-kernel aliasing, where similar observed distributions evolve differently under different contextual regimes, and prove that any forecaster depending only on an aliased summary incurs an irreducible weighted Jensen-Shannon excess-risk lower bound, while the CAST hypothesis class contains the regime-aware Bayes successor; for ordered supports an additional Pinsker separation holds whenever the transported successor lies outside the no-transport anchor hull. On eleven public and simulated benchmarks spanning ecology, energy, diet, mortality, employment, air quality, severe weather, mobility, and G/G/1, G_t/G/1 queue occupancy, CAST attains the best average rank on both one-step KL (1.27) and autoregressive rollout JSD (1.91), winning 8/11 sections on each metric against a broad statistical, compositional, recurrent, convolutional, and Transformer baseline set, and top-2 on all 11 sections for offline KL. Component ablations and a controlled synthetic aliasing experiment corroborate the theory.

Jiecheng Lu, Jieqi Di, Runhua Wu +1

Georgia Institute of Technology · Indiana University

Multivariate Time-Series Time Series Simplex Causal Transitions

May 15, 2026cs.LG

PESD-TSF: A Period-Aware and Explicit Structured Decomposition Framework for Long-Term Time Series Forecasting

Deep forecasting models often suffer from attenuated periodic perception and entangled trend-noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability, disrupts intrinsic dynamic coordination among variables, hindering the modeling of cross-variable consistency in multivariate time series. To address these issues, we propose PESD-TSF, a physics-inspired structured decomposition framework for long-term time series forecasting that jointly emphasizes interpretability and predictive accuracy. PESD-TSF introduces three key designs. First, a Multiplicative Periodic Gating mechanism incorporates continuous-time priors to dynamically modulate signal amplitudes, preserving periodic structures across deep layers. Second, a multi-scale structured encoder integrates detrended attention with hierarchical sampling to explicitly decouple long-term trends from high-frequency variations while retaining fine-grained temporal semantics. Third, to recover disrupted inter-variable dependencies, we propose Cross-Scale Collaborative Attention (CSCA) together with an RLC regularization scheme, which reconstructs global inter-variable topology in deep feature spaces and enforces physically consistent collaboration through orthogonality and consistency constraints. Extensive experiments on benchmark datasets from multiple domains demonstrate that PESD-TSF consistently achieves state-of-the-art performance, with particularly strong gains on multivariate forecasting tasks involving complex inter-variable coupling, highlighting its superior structural modeling capability and generalization.

Hua Wang, Xianhao Jiao, Fan Zhang

School of Computer and Artificial Intelligence, Ludong University, Yantai, Shandong 264025, China · School of Computer and Artificial Intelligence, Ludong University, Yantai, Shandong 264025, China. · School of Computer Science and Technology, Shandong Technology and Business University, Yantai, Shandong 264005, China +1

Multivariate Time Series Forecasting Multivariate Time-Series Long-Term

May 11, 2026cs.LG

HEPA: A Self-Supervised Horizon-Conditioned Event Predictive Architecture for Time Series

Critical events in multivariate time series, from turbine failures to cardiac arrhythmias, demand accurate prediction, yet labeled data is scarce because such events are rare and costly to annotate. We introduce HEPA (Horizon-conditioned Event Predictive Architecture), built on two key principles. First, a causal Transformer encoder is pretrained via a Joint-Embedding Predictive Architecture (JEPA): a horizon-conditioned predictor learns to forecast future representations rather than future values, forcing the encoder to capture predictable temporal dynamics from unlabeled data alone. Second, we freeze the encoder and finetune only the predictor toward the target event, producing a monotonic survival cumulative distribution function (CDF) over horizons. With fixed architecture and optimiser hyperparameters across all benchmarks, HEPA handles water contamination, cyberattack detection, volatility regimes, and eight further event types across 11 domains, exceeding leading time-series architectures including PatchTST, iTransformer, MAE, and Chronos-2 on at least 10 of 14 benchmarks, with an order of magnitude fewer tuned parameters and, on lifecycle datasets, an order of magnitude less labeled data.

Jonas Petersen, Gian-Alessandro Lombardi, Riccardo Maggioni +3

1ETH Zurich · 2Forgis · University of Vienna

Forecasting Backbone Multivariate Time-Series Time Series Transformer Encoder

May 11, 2026cs.LG

One-Step Graph-Structured Neural Flows for Irregular Multivariate Time Series Classification

Neural Flows efficiently model irregular multivariate time series by directly learning ODE solution trajectories with neural networks, bypassing step-by-step numerical solvers. Despite their efficiency, many existing approaches treat variables independently, leaving inter-variable interactions underexplored. Moreover, their one-step mapping makes interaction modeling inherently challenging, as it removes the iterative refinement of interactions during learning. To address this challenge, we propose one-step Graph-Structured Neural Flows (GSNF), which introduce two auxiliary-trajectory self-supervision strategies to strengthen interaction learning: (i) interaction-aware trajectory generation via re-initialization, which induces trajectory divergence to expose graph-induced interactions, with a theoretically derived lower bound on divergence; and (ii) reverse-time trajectory generation, which enforces forward-backward consistency to regularize graph learning, enabled by flow invertibility. Experiments on five real-world datasets show that GSNF achieves state-of-the-art classification performance with highly competitive training time and memory usage.

Mengzhou Gao, Kaiwei Wang, Pengfei Jiao

School of Cyberspace, Hangzhou Dianzi University.

Multivariate Time-Series Time-Series Classification

May 10, 2026cs.LG

Learning Unified Representations of Normalcy for Time Series Anomaly Detection

The core challenge in unsupervised anomaly detection is identifying abnormal patterns without prior knowledge of their characteristics. While existing methods have addressed aspects of this problem, they often struggle to learn a robust representation of the normal data distribution that is distinct from anomalous patterns. In this paper, we present a novel framework, Unified Unsupervised Anomaly Detection (

\text{U}^2\text{AD}

), that comprehensively addresses anomaly detection in multivariate time series. Our approach learns the underlying data distribution of normal samples by utilizing score-based generative modeling. We introduce a novel time-dependent score network and a unified training objective that together delineate the manifold of normal data while considering both local and global temporal contexts. Reconstruction is then performed via a deterministic sampling process using an ordinary differential equation solver. Our extensive experimental evaluations demonstrate that

\text{U}^2\text{AD}

not only outperforms current state-of-the-art methods in detection accuracy but also identifies anomalies at significantly earlier stages of their occurrence.

Prithul Sarker, Sushmita Sarker, Nicholas G. Murray +1

University of Nevada, Reno

Time-Series Anomaly Detection Graph Anomaly Detection Multivariate Time-Series Abnormality Norm

Apr 30, 2026cs.LG

Probabilistic Circuits for Irregular Multivariate Time Series Forecasting

Joint probabilistic modeling is essential for forecasting irregular multivariate time series (IMTS) to accurately quantify uncertainty. Existing approaches often struggle to balance model expressivity with consistent marginalization, frequently leading to unreliable or contradictory forecasts. To address this, we propose CircuITS, a novel architecture for probabilistic IMTS forecasting based on probabilistic circuits. Our model is flexible in capturing intricate dependencies between time series channels while structurally guaranteeing valid joint distributions. Experiments on four real world datasets demonstrate that CircuITS achieves superior joint and marginal density estimation compared to state of the art baselines.

Christian Klötergens, Vijaya Krishna Yalavarthi, Lars Schmidt-Thieme

1ISMLL, University of Hildesheim, Germany

Multivariate Time-Series Time Series Forecasting Probabilistic Model Circuits

Apr 17, 2026cs.LG

Univariate Channel Fusion for Multivariate Time Series Classification

Multivariate time series classification (MTSC) plays a crucial role in various domains, including biomedical signal analysis and motion monitoring. However, existing approaches, particularly deep learning models, often require high computational resources, making them unsuitable for real-time applications or deployment on low-cost hardware, such as IoT devices and wearable systems. In this paper, we propose the Univariate Channel Fusion (UCF) method to deal with MTSC efficiently. UCF transforms multivariate time series into a univariate representation through simple channel fusion strategies such as the mean, median, or dynamic time warping barycenter. This transformation enables the use of any classifier originally designed for univariate time series, providing a flexible and computationally lightweight alternative to complex models. We evaluate UCF in five case studies covering diverse application domains, including chemical monitoring, brain-computer interfaces, and human activity analysis. The results demonstrate that UCF often outperforms baseline methods and state-of-the-art algorithms tailored for MTSC, while achieving substantial gains in computational efficiency, being particularly effective in problems with high inter-channel correlation.

Fernando Moro, Vinicius M. A. Souza

Pontifícia Universidade Católica do Paraná (PUCPR), Brazil · Graduate Program in Informatics (PPGIa), Brazil

Time-Series Classification Multivariate Time-Series Deep Learning

Apr 14, 2026cs.AI

Fun-TSG: A Function-Driven Multivariate Time Series Generator with Variable-Level Anomaly Labeling

Reliable evaluation of anomaly detection methods in multivariate time series remains an open challenge, largely due to the limitations of existing benchmark datasets. Current resources often lack fine-grained anomaly annotations, do not provide explicit intervariable and temporal dependencies, and offer little insight into the underlying generative mechanisms. These shortcomings hinder the development and rigorous comparison of detection models, especially those targeting interpretable and variable-specific outputs. To address this gap, we introduce Fun-TSG, a fully customizable time series generator designed to support high-quality evaluation of anomaly detection systems. Our tool enables both fully automated generation, based on randomly sampled dependency structures and anomaly types, and manual generation through user-defined equations and anomaly configurations. In both cases, it provides full transparency over the data generation process, including access to ground-truth anomaly labels at the variable and timestamp levels. Fun-TSG supports the creation of diverse, interpretable, and reproducible benchmarking scenarios, enabling fine-grained performance analysis for both classical and modern anomaly detection models.

Pierre Lotte, André Péninou, Olivier Teste

EPE UT, IRIT · Université de Toulouse, IRIT, CNRS · UT2J, IRIT-SIG, IRIT +2

Time-Series Anomaly Detection Time-Series Generation Graph Anomaly Detection Multivariate Time-Series Generators Temporal Dependence

Mar 12, 2026cs.AI

Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal dynamics, and therefore can assign high probability to anomalous or out-of-distribution samples. We address this structural limitation by relocating the notion of anomaly to a prescribed latent space. We introduce explicit inductive biases in conditional normalizing flows, modeling time-series observations within a discrete-time state-space framework that constrains latent representations to evolve according to prescribed temporal dynamics. Under this formulation, expected behavior corresponds to compliance with a specified distribution over latent trajectories, while anomalies are defined as violations of these dynamics. Anomaly detection is consequently reformulated as a statistically grounded compliance test, such that observations are mapped to latent space and evaluated via goodness-of-fit tests against the prescribed latent evolution. This yields a principled decision rule that remains effective even in regions of high observation likelihood. Experiments on synthetic and real-world time-series demonstrate reliable detection of anomalies in frequency, amplitude, and observation noise, while providing interpretable diagnostics of model compliance.

David Baumgartner, Eliezer de Souza da Silva, Iñigo Urteaga

Department of Computer Science, Norwegian University of Science and Technology, Norway · BCAM — Basque Center for Applied Mathematics, Spain · Department of Informatics Engineering, University of Coimbra, Portugal +2

Time-Series Anomaly Detection Multivariate Time-Series Normalizing Flows Time Series Latent Space Latent Trajectories+1

Mar 12, 2026cs.LG

Deep Learning Network-Temporal Models For Traffic Prediction

Accurate prediction of multivariate time series is essential for emerging network intelligent control, observability, and management functions. Existing statistical-based and shallow machine learning models have shown limited prediction capabilities on multivariate time series. They prioritize improvements in average prediction accuracy, while overlooking heterogeneous dependency structures and performance variability across individual time series. Recent advances in large language models have introduced new directions for multivariate time series forecasting; however, their application in conjunction with explicit structural dependency modeling remains relatively underexplored, especially in networked environments. In this paper, we present a topology-aware learning framework for large-scale network traffic prediction that explicitly models both temporal dynamics and structural dependencies in multivariate network time series. We first investigate a graph attention model designed to capture topology-induced correlations among network traffic time series. We then evaluate a fine-tuned large language model-based representations for improved generalization across heterogeneous traffic patterns. To further address the diversity of cross-correlations in high-dimensional traffic data, we introduce a clustering-based preprocessing stage that groups traffic flows with similar dependency characteristics prior to model training, reducing input complexity and improving learning stability. Experiments on real backbone traffic data show consistent improvements over statistical and recurrent neural network baselines. In addition to average accuracy, we evaluate performance across individual time series and observe reduced variability in prediction quality.

Yufeng Xin, Ethan Fan

RENCI, University of North Carolina at Chapel Hill Chapel Hill, NC, USA

Accurate Traffic Forecasting Multivariate Time-Series Deep Learning Topology

Mar 6, 2026cs.LG

UniMamba: A Unified Spatial-Temporal Modeling Framework with State-Space and Attention Integration

Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.

Xingsheng Chen, Xianpei Mu, Deyu Yi +6

School of Computing and Data Science, The University of Hong Kong, Hong Kong, China · School of Information Engineering, Beijing Institute of Graphic Communication, Beijing, China · Innovation Engineering College, Macau University of Science and Technology, Macau, China +1

Multivariate Time Series Forecasting Spatio-Temporal Forecasting Multivariate Time-Series Spatiotemporal

Jun 25, 2025cs.LG

A foundation model with multi-variate parallel attention to generate neuronal activity

Learning from multi-variate time-series with heterogeneous channel configurations remains a fundamental challenge for deep neural networks, particularly in clinical domains such as intracranial electroencephalography (iEEG), where channel setups vary widely across subjects. In this work, we introduce multi-variate parallel attention (MVPA), a novel self-attention mechanism that disentangles content, temporal, and spatial attention, enabling flexible, generalizable, and efficient modeling of time-series data with varying channel counts and configurations. We use MVPA to build MVPFormer, a generative foundation model for human electrophysiology, trained to predict the evolution of iEEG signals across subjects. To support this and future efforts by the community, we release the SWEC iEEG dataset, the largest publicly available iEEG dataset to date, comprising nearly 10,000 hours of recordings from heterogeneous clinical sources. MVPFormer leverages MVPA to achieve strong generalization across subjects, demonstrating expert-level performance in several iEEG tasks. MVPFormer surpasses state-of-the-art (SOTA) Transformer baselines in seizure detection across the SWEC, the MAYO, and the FNUSA datasets, while also achieving SOTA performance on four Brain TreeBank iEEG decoding tasks (volume, pitch, onset, and speech). We further validate MVPA on standard time-series forecasting and classification tasks, where it matches or exceeds the performance of existing attention-based models. Together, our contributions establish MVPA as a general-purpose attention mechanism for heterogeneous time-series and MVPFormer as the first open-source, open-weights, and open-data iEEG foundation model with SOTA clinical performance. The code is available at https://github.com/IBM/multi-variate-parallel-transformer. The SWEC iEEG dataset is available at https://huggingface.co/datasets/NeuroTec/SWEC_iEEG_Dataset.

Francesco Carzaniga, Michael Hersche, Abu Sebastian +2

IBM Research – Zurich, Rüschlikon, Switzerland · Department of Neurology, Inselspital, Sleep-Wake-Epilepsy-Center, Bern University Hospital, Bern University, Bern, Switzerland

Multivariate Time-Series Temporal Attention Time Series Neural Circuits Foundation Model

Jun 2, 2025cs.LG

Temporal Variational Implicit Neural Representations

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient and accurate individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing INR approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs performs particularly well in low-data regimes, where on several datasets it achieves substantially lower imputation error, including order-of-magnitude improvements.

Batuhan Koyuncu, Rachael DeVries, Ole Winther +1

Department of Computer Science, Saarland University · Department of Biology, University of Copenhagen · Novo Nordisk A/S +1

Multivariate Time-Series Imputation Neural Representations Latent Variable