Topic:Time Series Analysis
What is Time Series Analysis? Time series analysis comprises statistical methods for analyzing a sequence of data points collected over an interval of time to identify interesting patterns and trends.
Papers and Code
Feb 05, 2025
Abstract:Universal knowledge representation is a central problem for multivariate time series(MTS) foundation models and yet remains open. This paper investigates this problem from the first principle and it makes four folds of contributions. First, a new empirical finding is revealed: time series with different time granularities (or corresponding frequency resolutions) exhibit distinct joint distributions in the frequency domain. This implies a crucial aspect of learning universal knowledge, one that has been overlooked by previous studies. Second, a novel Fourier knowledge attention mechanism is proposed to enable learning time granularity-aware representations from both the temporal and frequency domains. Third, an autoregressive blank infilling pre-training framework is incorporated to time series analysis for the first time, leading to a generative tasks agnostic pre-training strategy. To this end, we develop the General Time-series Model (GTM), a unified MTS foundation model that addresses the limitation of contemporary time series models, which often require token, pre-training, or model-level customizations for downstream tasks adaption. Fourth, extensive experiments show that GTM outperforms state-of-the-art (SOTA) methods across all generative tasks, including long-term forecasting, anomaly detection, and imputation.
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Feb 05, 2025
Abstract:We give a comprehensive analysis of transformers as time series foundation models, focusing on their approximation and generalization capabilities. First, we demonstrate that there exist transformers that fit an autoregressive model on input univariate time series via gradient descent. We then analyze MOIRAI, a multivariate time series foundation model capable of handling an arbitrary number of covariates. We prove that it is capable of automatically fitting autoregressive models with an arbitrary number of covariates, offering insights into its design and empirical success. For generalization, we establish bounds for pretraining when the data satisfies Dobrushin's condition. Experiments support our theoretical findings, highlighting the efficacy of transformers as time series foundation models.
* 34 Pages, 2 Figures
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Feb 05, 2025
Abstract:This paper investigates unsupervised anomaly detection in multivariate time-series data using reinforcement learning (RL) in the latent space of an autoencoder. A significant challenge is the limited availability of anomalous data, often leading to misclassifying anomalies as normal events, thus raising false negatives. RL can help overcome this limitation by promoting exploration and balancing exploitation during training, effectively preventing overfitting. Wavelet analysis is also utilized to enhance anomaly detection, enabling time-series data decomposition into both time and frequency domains. This approach captures anomalies at multiple resolutions, with wavelet coefficients extracted to detect both sudden and subtle shifts in the data, thereby refining the anomaly detection process. We calibrate the decision boundary by generating synthetic anomalies and embedding a supervised framework within the model. This supervised element aids the unsupervised learning process by fine-tuning the decision boundary and increasing the model's capacity to distinguish between normal and anomalous patterns effectively.
* This paper has been accepted for publication and presentation at the
2025 IEEE International systems Conference (SysCon)
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Feb 04, 2025
Abstract:We present a novel prompt design for Large Language Models (LLMs) tailored to Asynchronous Time Series. Unlike regular time series, which assume values at evenly spaced time points, asynchronous time series consist of timestamped events occurring at irregular intervals, each described in natural language. Our approach effectively utilizes the rich natural language of event descriptions, allowing LLMs to benefit from their broad world knowledge for reasoning across different domains and tasks. This allows us to extend the scope of asynchronous time series analysis beyond forecasting to include tasks like anomaly detection and data imputation. We further introduce Stochastic Soft Prompting, a novel prompt-tuning mechanism that significantly improves model performance, outperforming existing fine-tuning methods such as QLoRA. Through extensive experiments on real world datasets, we demonstrate that our approach achieves state-of-the-art performance across different tasks and datasets.
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Feb 03, 2025
Abstract:Understanding time series data is crucial for multiple real-world applications. While large language models (LLMs) show promise in time series tasks, current approaches often rely on numerical data alone, overlooking the multimodal nature of time-dependent information, such as textual descriptions, visual data, and audio signals. Moreover, these methods underutilize LLMs' reasoning capabilities, limiting the analysis to surface-level interpretations instead of deeper temporal and multimodal reasoning. In this position paper, we argue that multimodal LLMs (MLLMs) can enable more powerful and flexible reasoning for time series analysis, enhancing decision-making and real-world applications. We call on researchers and practitioners to leverage this potential by developing strategies that prioritize trust, interpretability, and robust reasoning in MLLMs. Lastly, we highlight key research directions, including novel reasoning paradigms, architectural innovations, and domain-specific applications, to advance time series reasoning with MLLMs.
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Feb 05, 2025
Abstract:Accurate forecasting of multivariate time series data is important in many engineering and scientific applications. Recent state-of-the-art works ignore the inter-relations between variates, using their model on each variate independently. This raises several research questions related to proper modeling of multivariate data. In this work, we propose to view multivariate forecasting as a multi-task learning problem, facilitating the analysis of forecasting by considering the angle between task gradients and their balance. To do so, we analyze linear models to characterize the behavior of tasks. Our analysis suggests that tasks can be defined by grouping similar variates together, which we achieve via a simple clustering that depends on correlation-based similarities. Moreover, to balance tasks, we scale gradients with respect to their prediction error. Then, each task is solved with a linear model within our MTLinear framework. We evaluate our approach on challenging benchmarks in comparison to strong baselines, and we show it obtains on-par or better results on multivariate forecasting problems. The implementation is available at: https://github.com/azencot-group/MTLinear
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Feb 05, 2025
Abstract:Effective anomaly detection in complex systems requires identifying change points (CPs) in the frequency domain, as abnormalities often arise across multiple frequencies. This paper extends recent advancements in statistically significant CP detection, based on Selective Inference (SI), to the frequency domain. The proposed SI method quantifies the statistical significance of detected CPs in the frequency domain using $p$-values, ensuring that the detected changes reflect genuine structural shifts in the target system. We address two major technical challenges to achieve this. First, we extend the existing SI framework to the frequency domain by appropriately utilizing the properties of discrete Fourier transform (DFT). Second, we develop an SI method that provides valid $p$-values for CPs where changes occur across multiple frequencies. Experimental results demonstrate that the proposed method reliably identifies genuine CPs with strong statistical guarantees, enabling more accurate root-cause analysis in the frequency domain of complex systems.
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Feb 04, 2025
Abstract:The integration of Large Language Models (LLMs) like GPT-4 with Extended Reality (XR) technologies offers the potential to build truly immersive XR environments that interact with human users through natural language, e.g., generating and animating 3D scenes from audio inputs. However, the complexity of XR environments makes it difficult to accurately extract relevant contextual data and scene/object parameters from an overwhelming volume of XR artifacts. It leads to not only increased costs with pay-per-use models, but also elevated levels of generation errors. Moreover, existing approaches focusing on coding script generation are often prone to generation errors, resulting in flawed or invalid scripts, application crashes, and ultimately a degraded user experience. To overcome these challenges, we introduce LLMER, a novel framework that creates interactive XR worlds using JSON data generated by LLMs. Unlike prior approaches focusing on coding script generation, LLMER translates natural language inputs into JSON data, significantly reducing the likelihood of application crashes and processing latency. It employs a multi-stage strategy to supply only the essential contextual information adapted to the user's request and features multiple modules designed for various XR tasks. Our preliminary user study reveals the effectiveness of the proposed system, with over 80% reduction in consumed tokens and around 60% reduction in task completion time compared to state-of-the-art approaches. The analysis of users' feedback also illuminates a series of directions for further optimization.
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Feb 05, 2025
Abstract:Following a recent study on the quality of OpenAlex linguistic metadata (C\'espedes et al., 2025), the present paper aims to optimize the latter through the design, use, and evaluation of various linguistic classification procedures based on the latest and most efficient automatic language detection algorithms. Starting from a multilingual set of manually-annotated samples of articles indexed in the database, different classification procedures are then designed, based on the application of a set of language detection algorithms on a series of corpora generated from different combinations of textual metadata of indexed articles. At sample level first, the performance of these different procedures for each of the main languages in the database is evaluated in terms of precision, recall, and processing time. Then, overall procedure performance is estimated at the database level by means of a probabilistic simulation of harmonically aggregated and weighted scores. Results show that procedure performance strongly depends on the importance given to each of the measures implemented: for contexts where precision is preferred, using the LangID algorithm on article titles, abstracts as well as journal names gives the best results; however, for all cases where recall is considered at least slightly more important than precision or as soon as processing times are given any kind of consideration, use of the FastSpell algorithm on article titles only outperforms all other alternatives. Given the lack of truly multilingual, large-scale bibliographic databases, it is hoped that these results help confirm and foster the unparalleled potential of the OpenAlex database for cross-linguistic, bibliometric-based research and analysis.
* 33 pages, 4 figures
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Feb 02, 2025
Abstract:The analysis of wearable sensor data has enabled many successes in several applications. To represent the high-sampling rate time-series with sufficient detail, the use of topological data analysis (TDA) has been considered, and it is found that TDA can complement other time-series features. Nonetheless, due to the large time consumption and high computational resource requirements of extracting topological features through TDA, it is difficult to deploy topological knowledge in various applications. To tackle this problem, knowledge distillation (KD) can be adopted, which is a technique facilitating model compression and transfer learning to generate a smaller model by transferring knowledge from a larger network. By leveraging multiple teachers in KD, both time-series and topological features can be transferred, and finally, a superior student using only time-series data is distilled. On the other hand, mixup has been popularly used as a robust data augmentation technique to enhance model performance during training. Mixup and KD employ similar learning strategies. In KD, the student model learns from the smoothed distribution generated by the teacher model, while mixup creates smoothed labels by blending two labels. Hence, this common smoothness serves as the connecting link that establishes a connection between these two methods. In this paper, we analyze the role of mixup in KD with time-series as well as topological persistence, employing multiple teachers. We present a comprehensive analysis of various methods in KD and mixup on wearable sensor data.
* IEEE Sensors Journal (2024)
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