An Encode-then-Decompose Approach to Unsupervised Time Series Anomaly Detection on Contaminated Training Data--Extended Version

Time series anomaly detection is important in modern large-scale systems and is applied in a variety of domains to analyze and monitor the operation of diverse systems. Unsupervised approaches have received widespread interest, as they do not require anomaly labels during training, thus avoiding potentially high costs and having wider applications. Among these, autoencoders have received extensive attention. They use reconstruction errors from compressed representations to define anomaly scores. However, representations learned by autoencoders are sensitive to anomalies in training time series, causing reduced accuracy. We propose a novel encode-then-decompose paradigm, where we decompose the encoded representation into stable and auxiliary representations, thereby enhancing the robustness when training with contaminated time series. In addition, we propose a novel mutual information based metric to replace the reconstruction errors for identifying anomalies. Our proposal demonstrates competitive or state-of-the-art performance on eight commonly used multi- and univariate time series benchmarks and exhibits robustness to time series with different contamination ratios.

Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective

Time Series Forecasting has made significant progress with the help of Patching technique, which partitions time series into multiple patches to effectively retain contextual semantic information into a representation space beneficial for modeling long-term dependencies. However, conventional patching partitions a time series into adjacent patches, which causes a fixed representation space, thus resulting in insufficiently expressful representations. In this paper, we pioneer the exploration of constructing a selective representation space to flexibly include the most informative patches for forecasting. Specifically, we propose the Selective Representation Space (SRS) module, which utilizes the learnable Selective Patching and Dynamic Reassembly techniques to adaptively select and shuffle the patches from the contextual time series, aiming at fully exploiting the information of contextual time series to enhance the forecasting performance of patch-based models. To demonstrate the effectiveness of SRS module, we propose a simple yet effective SRSNet consisting of SRS and an MLP head, which achieves state-of-the-art performance on real-world datasets from multiple domains. Furthermore, as a novel plugin-and-play module, SRS can also enhance the performance of existing patch-based models. The resources are available at https://github.com/decisionintelligence/SRSNet.

Unlocking the Power of Mixture-of-Experts for Task-Aware Time Series Analytics

Time Series Analysis is widely used in various real-world applications such as weather forecasting, financial fraud detection, imputation for missing data in IoT systems, and classification for action recognization. Mixture-of-Experts (MoE), as a powerful architecture, though demonstrating effectiveness in NLP, still falls short in adapting to versatile tasks in time series analytics due to its task-agnostic router and the lack of capability in modeling channel correlations. In this study, we propose a novel, general MoE-based time series framework called PatchMoE to support the intricate ``knowledge'' utilization for distinct tasks, thus task-aware. Based on the observation that hierarchical representations often vary across tasks, e.g., forecasting vs. classification, we propose a Recurrent Noisy Gating to utilize the hierarchical information in routing, thus obtaining task-sepcific capability. And the routing strategy is operated on time series tokens in both temporal and channel dimensions, and encouraged by a meticulously designed Temporal \& Channel Load Balancing Loss to model the intricate temporal and channel correlations. Comprehensive experiments on five downstream tasks demonstrate the state-of-the-art performance of PatchMoE.

DAG: A Dual Causal Network for Time Series Forecasting with Exogenous Variables

Time series forecasting is crucial in various fields such as economics, traffic, and AIOps. However, in real-world applications, focusing solely on the endogenous variables (i.e., target variables), is often insufficient to ensure accurate predictions. Considering exogenous variables (i.e., covariates) provides additional predictive information, thereby improving forecasting accuracy. However, existing methods for time series forecasting with exogenous variables (TSF-X) have the following shortcomings: 1) they do not leverage future exogenous variables, 2) they fail to account for the causal relationships between endogenous and exogenous variables. As a result, their performance is suboptimal. In this study, to better leverage exogenous variables, especially future exogenous variable, we propose a general framework DAG, which utilizes dual causal network along both the temporal and channel dimensions for time series forecasting with exogenous variables. Specifically, we first introduce the Temporal Causal Module, which includes a causal discovery module to capture how historical exogenous variables affect future exogenous variables. Following this, we construct a causal injection module that incorporates the discovered causal relationships into the process of forecasting future endogenous variables based on historical endogenous variables. Next, we propose the Channel Causal Module, which follows a similar design principle. It features a causal discovery module models how historical exogenous variables influence historical endogenous variables, and a causal injection module incorporates the discovered relationships to enhance the prediction of future endogenous variables based on future exogenous variables.

$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting

Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). As the forecast horizon extends, the inherent nonlinear dynamics have a significant adverse effect on prediction accuracy, and make generative models inefficient by increasing the cost of each iteration. To overcome these limitations, we introduce $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.

Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline

The forecasting of irregular multivariate time series (IMTS) is crucial in key areas such as healthcare, biomechanics, climate science, and astronomy. However, achieving accurate and practical predictions is challenging due to two main factors. First, the inherent irregularity and data missingness in irregular time series make modeling difficult. Second, most existing methods are typically complex and resource-intensive. In this study, we propose a general framework called APN to address these challenges. Specifically, we design a novel Time-Aware Patch Aggregation (TAPA) module that achieves adaptive patching. By learning dynamically adjustable patch boundaries and a time-aware weighted averaging strategy, TAPA transforms the original irregular sequences into high-quality, regularized representations in a channel-independent manner. Additionally, we use a simple query module to effectively integrate historical information while maintaining the model's efficiency. Finally, predictions are made by a shallow MLP. Experimental results on multiple real-world datasets show that APN outperforms existing state-of-the-art methods in both efficiency and accuracy.

EasyTime: Time Series Forecasting Made Easy

Time series forecasting has important applications across diverse domains. EasyTime, the system we demonstrate, facilitates easy use of time-series forecasting methods by researchers and practitioners alike. First, EasyTime enables one-click evaluation, enabling researchers to evaluate new forecasting methods using the suite of diverse time series datasets collected in the preexisting time series forecasting benchmark (TFB). This is achieved by leveraging TFB's flexible and consistent evaluation pipeline. Second, when practitioners must perform forecasting on a new dataset, a nontrivial first step is often to find an appropriate forecasting method. EasyTime provides an Automated Ensemble module that combines the promising forecasting methods to yield superior forecasting accuracy compared to individual methods. Third, EasyTime offers a natural language Q&A module leveraging large language models. Given a question like "Which method is best for long term forecasting on time series with strong seasonality?", EasyTime converts the question into SQL queries on the database of results obtained by TFB and then returns an answer in natural language and charts. By demonstrating EasyTime, we intend to show how it is possible to simplify the use of time series forecasting and to offer better support for the development of new generations of time series forecasting methods.

DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting

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 \textbf{DUET}, which introduces \underline{DU}al clustering on the temporal and channel dimensions to \underline{E}nhance multivariate \underline{T}ime 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.

MultiRC: Joint Learning for Time Series Anomaly Prediction and Detection with Multi-scale Reconstructive Contrast

Many methods have been proposed for unsupervised time series anomaly detection. Despite some progress, research on predicting future anomalies is still relatively scarce. Predicting anomalies is particularly challenging due to the diverse reaction time and the lack of labeled data. To address these challenges, we propose MultiRC to integrate reconstructive and contrastive learning for joint learning of anomaly prediction and detection, with multi-scale structure and adaptive dominant period mask to deal with the diverse reaction time. MultiRC also generates negative samples to provide essential training momentum for the anomaly prediction tasks and prevent model degradation. We evaluate seven benchmark datasets from different fields. For both anomaly prediction and detection tasks, MultiRC outperforms existing state-of-the-art methods.

DiffImp: Efficient Diffusion Model for Probabilistic Time Series Imputation with Bidirectional Mamba Backbone

Probabilistic time series imputation has been widely applied in real-world scenarios due to its ability to estimate uncertainty of imputation results. Meanwhile, 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)~\textit{~The backbone modules of the denoising parts are not capable of achieving sequence modeling with low time complexity.} 2)~\textit{The architecture of denoising modules can not handle the inter-variable and bidirectional dependencies in the time series imputation problem effectively.} To address the first challenge, we integrate the computational efficient state space model, namely Mamba, as the backbone denosing module for DDPMs. To tackle the second challenge, we carefully devise several SSM-based blocks for bidirectional modeling and inter-variable relation understanding. Experimental results demonstrate that our approach can achieve state-of-the-art time series imputation results on multiple datasets, different missing scenarios and missing ratios.