Classical time-series forecasting methods rely on learning from a fixed context window of past observations and extrapolating to a fixed number of future steps. They are therefore limited in flexibility and effectiveness in modeling tasks of varying historical lengths or future horizons, requiring re-training for each setting. We propose Contextual Meta-Adaptation (CMA), a unified scheme that captures history contexts and extrapolates future horizons with a single training. CMA integrates denoising diffusion capability which can sequentially generate a future series with maximum likelihood and remains consistent with observed history and past generations. We develop an efficient update strategy using gradient-based meta-learning for full-parameter tuning during training and LoRA adaptation at testing time. We validate our CMA scheme on in-context learning with longer observed history, ex(tend)-context learning with up to 3 times longer future horizons, and transfer-learning across different source-target domains. Our CMA outperforms existing methods by an average of 7% on six academic datasets and a significant 16% improvement on four realistic marketing datasets.
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Time series anomaly detection (TSAD) is a central topic in data mining, with many algorithms proposed, including deep learning and LLM-based methods. However, these are often evaluated on flawed benchmarks with trivial anomalies, unrealistic densities, mislabeled ground truth, and run-to-failure biases. Recent studies using higher-quality datasets show that simpler distance-based methods, such as discords, can outperform deep learning; However, they typically rely on sliding windows with fixed lengths, limiting flexibility. We introduce GDFlex (Generalized Discords with Flexible Subsequence Length), a discord-based method that detects anomalies across multiple time scales using length-normalized Euclidean distance. It also incorporates bias-correction mechanisms to address limitations in Euclidean distance and z-normalization. GDFlex achieves notable accuracy gains over existing methods while remaining scalable, interpretable, and efficient.
MetaEformer: Unveiling and Leveraging Meta-Patterns for Complex and Dynamic Systems Load Forecasting
Time series forecasting is a critical and practical problem in many real-world applications, especially for industrial scenarios, where load forecasting underpins the intelligent operation of modern systems like clouds, power grids and traffic networks. However, the inherent complexity and dynamics of these systems present significant challenges. Despite advances in methods such as pattern recognition and anti-non-stationarity have led to performance gains, current methods fail to consistently ensure effectiveness across various system scenarios due to the intertwined issues of complex patterns, concept-drift, and few-shot problems. To address these challenges simultaneously, we introduce a novel scheme centered on fundamental waveform, a.k.a., meta-pattern. Specifically, we develop a unique Meta-pattern Pooling mechanism to purify and maintain meta-patterns, capturing the nuanced nature of system loads. Complementing this, the proposed Echo mechanism adaptively leverages the meta-patterns, enabling a flexible and precise pattern reconstruction. Our Meta-pattern Echo transformer (MetaEformer) seamlessly incorporates these mechanisms with the transformer-based predictor, offering end-to-end efficiency and interpretability of core processes. Demonstrating superior performance across eight benchmarks under three system scenarios, MetaEformer marks a significant advantage in accuracy, with a 37% relative improvement on fifteen state-of-the-art baselines.
Variable Subset Forecasting (VSF) poses critical challenges in time series analysis when entire variables become unavailable during inference. Existing imputation methods relying on inter-variable correlations fail catastrophically in VSF due to two inherent limitations: (1) Missing variable collapse, where the complete absence of certain variables invalidates correlation-based dependency learning, and (2) Temporal covariate shift, where time-evolving data distributions destabilize correlation patterns learned from training data. To address these fundamental issues, we propose Generative Imputation with Multi-level Causal Consistency (GIMCC ), establishing causality-driven imputation as the first principled solution for VSF. Our key innovation lies in enforcing causal invariance through dual consistency constraints: global causal isomorphism ensures the imputed variables preserve the ground-truth causal graph structure of the complete system, while local causal subgraph alignment maintains consistency between observed variables and their causal neighborhood dependencies. By decoupling causality from spurious correlations, GIMCC provides time-invariant imputation signals robust to distribution shifts, which explicitly preserves causal relationships via multivariate spectral convolutions. Extensive experiments across five real-world domains demonstrate that GIMCC achieves average improvements of 20-60% in MAE/RMSE over correlation-based imputation baselines, remarkably outperforming full-variable training ( Oracle ) in temporal covariate shift scenarios. Our work bridges the critical gap between causal analysis and practical forecasting systems under variable absence, offering theoretically grounded guarantees for real-world deployment.
Temporal Restoration and Spatial Rewiring for Source-Free Multivariate Time Series Domain Adaptation
Source-Free Domain Adaptation (SFDA) aims to adapt a pre-trained model from an annotated source domain to an unlabelled target domain without accessing the source data, thereby preserving data privacy. While existing SFDA methods have proven effective in reducing reliance on source data, they struggle to perform well on multivariate time series (MTS) due to their failure to consider the intrinsic spatial correlations inherent in MTS data. These spatial correlations are crucial for accurately representing MTS data and preserving invariant information across domains. To address this challenge, we propose Temporal Restoration and Spatial Rewiring (TERSE), a novel and concise SFDA method tailored for MTS data. Specifically, TERSE comprises a customized spatial-temporal feature encoder designed to capture the underlying spatial-temporal characteristics, coupled with both temporal restoration and spatial rewiring tasks to reinstate latent representations of the temporally masked time series and the spatially masked correlated structures. During the target adaptation phase, the target encoder is guided to produce spatially and temporally consistent features with the source domain by leveraging the source pre-trained temporal restoration and spatial rewiring networks. Therefore, TERSE can effectively model and transfer spatial-temporal dependencies across domains, facilitating implicit feature alignment. In addition, as the first approach to simultaneously consider spatial-temporal consistency in MTS-SFDA, TERSE can also be integrated as a versatile plug-and-play module into established SFDA methods. Extensive experiments on three real-world time series datasets demonstrate the effectiveness and versatility of our approach. Our code is available at https://github.com/Tokenmw/TERSE-master.
Probabilistic time series imputation has been widely applied in real-world scenarios due to its ability for uncertainty estimation and denoising diffusion probabilistic models (DDPMs) have achieved great success in probabilistic time series imputation tasks with its power to model complex distributions. However, current DDPM-based probabilistic time series imputation methodologies are confronted with two types of challenges: 1) The backbone modules of the denoising parts are not capable of achieving sequence modeling with low time complexity. 2) The architecture of denoising modules can not handle the dependencies in the time series data effectively. To address the first challenge, we explore the potential of state space model, namely Mamba, as the backbone denoising module for DDPMs. To tackle the second challenge, we carefully devise several SSM-based blocks for time series data modeling. Experimental results demonstrate that our approach can achieve state-of-the-art time series imputation results on multiple real-world datasets. Our datasets and code are available at https://github.com/decisionintelligence/SSD-TS/
Synthetic Electronic Health Record (EHR) time-series generation is crucial for advancing clinical machine learning models, as it helps address data scarcity by providing more training data. However, most existing approaches focus primarily on replicating statistical distributions and temporal dependencies of real-world data. We argue that fidelity to observed data alone does not guarantee better model performance, as common patterns may dominate, limiting the representation of rare but important conditions. This highlights the need for generate synthetic samples to improve performance of specific clinical models to fulfill their target outcomes. To address this, we propose TarDiff, a novel target-oriented diffusion framework that integrates task-specific influence guidance into the synthetic data generation process. Unlike conventional approaches that mimic training data distributions, TarDiff optimizes synthetic samples by quantifying their expected contribution to improving downstream model performance through influence functions. Specifically, we measure the reduction in task-specific loss induced by synthetic samples and embed this influence gradient into the reverse diffusion process, thereby steering the generation towards utility-optimized data. Evaluated on six publicly available EHR datasets, TarDiff achieves state-of-the-art performance, outperforming existing methods by up to 20.4% in AUPRC and 18.4% in AUROC. Our results demonstrate that TarDiff not only preserves temporal fidelity but also enhances downstream model performance, offering a robust solution to data scarcity and class imbalance in healthcare analytics.
Recent advancements in time-series forecasting have highlighted the importance of frequency-domain modeling. However, deep learning models primarily operate in the time domain, limiting their ability to capture frequency-based patterns. Existing approaches normally introduce novel neural network architectures tailored to task-specific frequency properties, yet they often lack generalization and require extensive domain-specific adaptations. In this paper, we propose FAT, a novel pretraining framework that learns generalizable Frequency-Aware Time-series representations through self-supervised learning. The key idea of FAT is to pretrain any backbone model to directly extract generalizable frequency patterns from time-domain signals and encode them into robust representations-eliminating the need for architectural modifications or additional modules during inference. This is achieved via a frequency reformer that amplifies critical frequency components learned through self-supervision and enforces similarity between the original and frequency-reformed time-series representations produced by the encoder. In addition, recognizing that semantically equivalent time-series can exhibit different frequency expressions-analogous to how the same phrase is pronounced differently by different speakers-FAT introduces a Knowledge-Guided Frequency Reformer that unifies the expression of frequency patterns with the same underlying semantics and extends similarity constraints to frequency-invariant augmented samples to enhance robustness of learned representation. Experiments on 14 benchmark datasets across regression and classification tasks show that FAT consistently achieves state-of-the-art performance while maintaining robustness across diverse backbone models, significantly outperforming existing pretraining methods. Our code is available at https://github.com/JiaXiangfei/FAT.
Time series anomaly detection has garnered significant research attention due to growing demands for temporal data monitoring across diverse domains. Despite the rapid advent of unsupervised anomaly detection models, existing approaches face two critical challenges in understanding the mechanisms of reconstruction-based models when handling diverse temporal dependencies: (1) the insufficient exploration of complex inter-timestamp relationships encompassing both short-term and long-term dependencies, and (2) the lack of integrated frameworks for jointly learning short-term patterns and long-term temporal characteristics. To address these challenges, we propose the novel Multi-Scale Hypergraph Transformer (MSHTrans), which leverages the capacity of hypergraphs for modeling multi-order temporal dependencies. Particularly, our method employs multi-scale downsampling to derive complementary fine-grained and coarse-grained representations, integrated with trainable hypergraph neural networks that can adaptively learn inter-timestamp relationships. The framework further integrates time series decomposition to systematically extract periodic and trend components from multi-granular features, thereby enhancing long-term dependency modeling. Through synergistic integration of learned short-term patterns and long-term temporal structures, the model achieves comprehensive time series reconstruction for effective anomaly detection. Extensive experiments demonstrate that MSHTrans outperforms state-of-the-art competitors with an average performance improvement of 8.21% (without point adjustment) and 3.52% (with point adjustment).
Time series forecasting is important in finance domain. Financial time series (TS) patterns are influenced by both short-term public opinions and medium-/long-term policy and market trends. Hence, processing multi-period inputs becomes crucial for accurate financial time series forecasting (TSF). However, current TSF models either use only single-period input, or lack customized designs for addressing multi-period characteristics. In this paper, we propose a Multi-period Learning Framework (MLF) to enhance financial TSF performance. MLF considers both TSF's accuracy and efficiency requirements. Specifically, we design three new modules to better integrate the multi-period inputs for improving accuracy: (i) Inter-period Redundancy Filtering (IRF), that removes the information redundancy between periods for accurate self-attention modeling, (ii) Learnable Weighted-average Integration (LWI), that effectively integrates multi-period forecasts, (iii) Multi-period self-Adaptive Patching (MAP), that mitigates the bias towards certain periods by setting the same number of patches across all periods. Furthermore, we propose a Patch Squeeze module to reduce the number of patches in self-attention modeling for maximized efficiency. MLF incorporates multiple inputs with varying lengths (periods) to achieve better accuracy and reduces the costs of selecting input lengths during training. The codes and datasets are available at https://github.com/Meteor-Stars/MLF.
Encrypted traffic classification occupies a significant role in cybersecurity and network management. The existing encrypted traffic classification technology mostly relies on intra-flow semantics for extracting features. However, considering that some attack behaviors inherently have similar patterns to legitimate behaviors, and powerful adversaries could simulate benign users to conceal their attack intentions, intra-flow features may be similar between different categories. In this paper, we propose TrafficScope, a time-wavelet fusion network based on Transformer to enhance the performance of encrypted traffic classification. Specifically, in addition to using intra-flow semantics, TrafficScope also extracts contextual information to construct more comprehensive representations. Moreover, to cope with the non-stationary and dynamic contextual traffic, we employ wavelet transform to extract invariant features. For feature fusion, the cross-attention mechanism is adopted to inline combine temporal and wavelet-domain features. We extensively evaluate TrafficScope compared with 7 state-of-the-art baselines based on four groups of real-world traffic datasets, the results show that TrafficScope outperforms existing methods. We conduct a series of experiments in terms of similar intra-flow feature evaluation, data pollution, flow manipulations, and dynamic context to demonstrate the robustness and stability of the proposed method. Furthermore, we produce additional experiments to present the potential of TrafficScope in cross-dataset scenarios.
Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present Proceed, a novel proactive model adaptation framework for online time series forecasting. Proceed first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, Proceed is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that Proceed brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at https://github.com/SJTU-DMTai/OnlineTSF.
Learning low-dimensional semantic representations in diffusion models (DMs) is an open task, since in standard DMs, the dimensions of its intermediate latents are the same as that of the observations and thus are unable to represent low-dimensional semantics. Existing methods address this task either by encoding observations into semantics which makes it difficult to generate samples without observations, or by synthesizing the U-Net's layers of pre-trained DMs into low-dimensional semantics, which is mainly used for downstream tasks rather than using semantics to facilitate the training process. Further, those generated static representations might not be aligned with dynamic timestep-wise intermediate latents. This work introduces a Progressive self-encoded Diffusion model (ProgDiffusion), which simultaneously learns semantic representations and reconstructs observations, does efficient unconditional generation, and produces progressively structured semantic representations. These benefits are gained by a novel self-encoder mechanism which takes the U-Net's upsampling features, intermediate latent and the denoising timestep as conditions to generate time-specific semantic representations, differing from existing work of conditioning on observations only. As a result, the learned intermediate latents are dynamic and mapped to a series of semantic representations that capture their gradual changes. Notably, our proposed encoder operates independently of the observations, making it feasible for unconditional generation as observations are not required. To evaluate ProgDiffusion, we design tasks to visualise the learned progressive semantic representations, in addition to other common tasks, which validate the effectiveness of ProgDiffusion against the state-of-the-art. The code is available at https://github.com/amasawa/ProgDiffusion.
Detecting anomalies in temporal data has gained significant attention across various real-world applications, aiming to identify unusual events and mitigate potential hazards. In practice, situations often involve a mix of segment-level labels (detected abnormal events with segments of time points) and unlabeled data (undetected events), while the ideal algorithmic outcome should be point-level predictions. Therefore, the huge label information gap between training data and targets makes the task challenging. In this study, we formulate the above imperfect information as noisy labels and propose NRdetector, a noise-resilient framework that incorporates confidence-based sample selection, robust segment-level learning, and data-centric point-level detection for multivariate time series anomaly detection. Particularly, to bridge the information gap between noisy segment-level labels and missing point-level labels, we develop a novel loss function that can effectively mitigate the label noise and consider the temporal features. It encourages the smoothness of consecutive points and the separability of points from segments with different labels. Extensive experiments on real-world multivariate time series datasets with 11 different evaluation metrics demonstrate that NRdetector consistently achieves robust results across multiple real-world datasets, outperforming various baselines adapted to operate in our setting.
We study the novel problem of future off-policy evaluation (F-OPE) and learning (F-OPL) for estimating and optimizing the future value of policies in non-stationary environments, where distributions vary over time. In e-commerce recommendations, for instance, our goal is often to estimate and optimize the policy value for the upcoming month using data collected by an old policy in the previous month. A critical challenge is that data related to the future environment is not observed in the historical data. Existing methods assume stationarity or depend on restrictive reward-modeling assumptions, leading to significant bias. To address these limitations, we propose a novel estimator named Off-Policy Estimator for the Future Value (OPFV), designed for accurately estimating policy values at any future time point. The key feature of OPFV is its ability to leverage the useful structure within time-series data. While future data might not be present in the historical log, we can leverage, for example, seasonal, weekly, or holiday effects that are consistent in both the historical and future data. Our estimator is the first to exploit these time-related structures via a new type of importance weighting, enabling effective F-OPE. Theoretical analysis identifies the conditions under which OPFV becomes low-bias. In addition, we extend our estimator to develop a new policy-gradient method to proactively learn a good future policy using only historical data. Empirical results show that our methods substantially outperform existing methods in estimating and optimizing the future policy value under non-stationarity for various experimental setups.
Forecasting complex time series is an important yet challenging problem that involves various industrial applications. Recently, masked time-series modeling has been proposed to effectively model temporal dependencies for forecasting by reconstructing masked segments from unmasked ones. However, since the semantic information in time series is involved in intricate temporal variations generated by multiple time series components, simply masking a raw time series ignores the inherent semantic structure, which may cause MTM to learn spurious temporal patterns present in the raw data. To capture distinct temporal semantics, we show that masked modeling techniques should address entangled patterns through a decomposition approach. Specifically, we propose ST-MTM, a masked time-series modeling framework with seasonal-trend decomposition, which includes a novel masking method for the seasonal-trend components that incorporates different temporal variations from each component. ST-MTM uses a period masking strategy for seasonal components to produce multiple masked seasonal series based on inherent multi-periodicity and a sub-series masking strategy for trend components to mask temporal regions that share similar variations. The proposed masking method presents an effective pre-training task for learning intricate temporal variations and dependencies. Additionally, ST-MTM introduces a contrastive learning task to support masked modeling by enhancing contextual consistency among multiple masked seasonal representations. Experimental results show that our proposed ST-MTM achieves consistently superior forecasting performance compared to existing masked modeling, contrastive learning, and supervised forecasting methods.
Multivariate time series forecasting is crucial for various applications, such as financial investment, energy management, weather forecasting, and traffic optimization. However, accurate forecasting is challenging due to two main factors. First, real-world time series often show heterogeneous temporal patterns caused by distribution shifts over time. Second, correlations among channels are complex and intertwined, making it hard to model the interactions among channels precisely and flexibly. In this study, we address these challenges by proposing a general framework called DUET, which introduces DU al clustering on the temporal and channel dimensions to Enhance multivariate Time series forecasting. First, we design a Temporal Clustering Module (TCM) that clusters time series into fine-grained distributions to handle heterogeneous temporal patterns. For different distribution clusters, we design various pattern extractors to capture their intrinsic temporal patterns, thus modeling the heterogeneity. Second, we introduce a novel Channel-Soft-Clustering strategy and design a Channel Clustering Module (CCM), which captures the relationships among channels in the frequency domain through metric learning and applies sparsification to mitigate the adverse effects of noisy channels. Finally, DUET combines TCM and CCM to incorporate both the temporal and channel dimensions. Extensive experiments on 25 real-world datasets from 10 application domains, demonstrate the state-of-the-art performance of DUET.
The time-index models are a class of time series forecasting models that map time-index features to forecasts in continuous space. Compared to the historical-value models, the time-index models can avoid the effect of data sampling frequency and are usually more expressive. However, the vanilla deep time-index model is weak in modeling the high-frequency components of time series and often requires the introduction of many parameters to enhance the modeling capability. Moreover, the time-index model learns only a mapping relationship and ignores the sequence relationship between temporal features, leading to a weak extrapolation capability in the forecast horizon. In this paper, inspired by the ability of quantum implicit neural representations to model the high-frequency components of signals with fewer parameters, we propose Quantum Time-Index Models with Reservoir (QuantumTime). Specifically, we introduce variational quantum circuits to address the challenge of representing high-frequency components in time series. Then, we introduce a reservoir that empowers QuantumTime with powerful extrapolation capabilities by exploiting the rich dynamical properties of reservoir computing. Ultimately, experiments conducted on chaotic datasets and various real-world datasets demonstrate that QuantumTime achieves highly competitive results compared to the state-of-the-art deep time-index model while reducing training parameters by at least 95%. Our approach provides a paradigm for utilizing potential quantum advantage in practical tasks.
Time series anomaly detection aims to identify unusual patterns in data or deviations from systems' expected behavior. The reconstruction-based methods are the mainstream in this task, which learn point-wise representation via unsupervised learning. However, the unlabeled anomaly points in training data may cause these reconstruction-based methods to learn and reconstruct anomalous data, resulting in the challenge of capturing normal patterns. In this paper, we propose a time series anomaly detection method based on implicit neural representation (INR) reconstruction, named TSINR, to address this challenge. Due to the property of spectral bias, TSINR enables prioritizing low-frequency signals and exhibiting poorer performance on high-frequency abnormal data. Specifically, we adopt INR to parameterize time series data as a continuous function and employ a transformer-based architecture to predict the INR of given data. As a result, the proposed TSINR method achieves the advantage of capturing the temporal continuity and thus is more sensitive to discontinuous anomaly data. In addition, we further design a novel form of INR continuous function to learn inter- and intra-channel information, and leverage a pre-trained large language model to amplify the intense fluctuations in anomalies. Extensive experiments demonstrate that TSINR achieves superior overall performance on both univariate and multivariate time series anomaly detection benchmarks compared to other state-of-the-art reconstruction-based methods. Our codes are available here.
Large quantities of social activity data, such as weekly web search volumes and the number of new infections with infectious diseases, reflect peoples' interests and activities. It is important to discover temporal patterns from such data and to forecast future activities accurately. However, modeling and forecasting social activity data streams is difficult because they are high-dimensional and composed of multiple time-varying dynamics such as trends, seasonality, and interest diffusion. In this paper, we propose D-Tracker, a method for continuously capturing time-varying temporal patterns within social activity tensor data streams and forecasting future activities. Our proposed method has the following properties: (a) Interpretable: it incorporates the partial differential equation into a tensor decomposition framework and captures time-varying temporal patterns such as trends, seasonality, and interest diffusion between locations in an interpretable manner; (b) Automatic: it has no hyperparameters and continuously models tensor data streams fully automatically; (c) Scalable: the computation time of D-Tracker is independent of the time series length. Experiments using web search volume data obtained from GoogleTrends, and COVID-19 infection data obtained from COVID-19 Open Data Repository show that our method can achieve higher forecasting accuracy in less computation time than existing methods while extracting the interest diffusion between locations. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/D-Tracker.