Abstract-- Detecting anomalies in multivariate time series is essential for monitoring complex industrial systems, where high dimensionality, limited labeled data, and subtle dependencies between sensors cause significant challenges. This paper presents a deep reinforcement learning framework that combines a V ari-ational Autoencoder (V AE), an LSTM-based Deep Q-Network (DQN), dynamic reward shaping, and an active learning module to address these issues in a unified learning framework. The main contribution is the implementation of Dynamic Reward Scaling for Multivariate Time Series Anomaly Detection (DRSMT), which demonstrates how each component enhances the detection process. The V AE captures compact latent representations and reduces noise. The DQN enables adaptive, sequential anomaly classification, and the dynamic reward shaping balances exploration and exploitation during training by adjusting the importance of reconstruction and classification signals. In addition, active learning identifies the most uncertain samples for labeling, reducing the need for extensive manual supervision. Experiments on two multivariate benchmarks, namely Server Machine Dataset (SMD) and Water Distribution T estbed (W ADI), show that the proposed method outperforms existing baselines in F1-score and AU-PR. In many of today's applications, identifying and removing anomalies (i.e., outliers) has become essential to ensure system reliability. In multivariate time series data, specifically, different factors can result in anomalies.

Granger Causality (GC) offers an elegant statistical framework to study the association between multivariate time series data. Linear Vector Autoregressive models (VAR) though have nice interpretation properties but have limited practical application due to underlying assumptions on the kind of associations that can be captured by these models. Numerous attempts have already been made in the literature that exploit the functional approximation power of Deep Neural Networks (DNNs) for the task of GC estimation. These methods however treat GC as a variable selection problem. We present a novel paradigm for approaching GC. We present this idea that GC is essentially linked with prediction and if a deep learning model is used to model the time series collectively or jointly, a well regularized model may learn the true granger causal structure from the data, given that there is enough training data. We propose to uncover the learned GC structure by comparing the model uncertainty or distribution of the residuals when the past of everything is used as compared to the one where a specific time series component is dropped from the model. We also compare the effect of input layer dropout on the ability of a neural network to learn granger causality from the data. We show that a well regularized model infact can learn the true GC structure from the data without explicitly adding terms in the loss function that guide the model to select variables or perform sparse regression.

Traditional solar flare forecasting approaches have mostly relied on physics-based or data-driven models using solar magnetograms, treating flare predictions as a point-in-time classification problem. This approach has limitations, particularly in capturing the evolving nature of solar activity. Recognizing the limitations of traditional flare forecasting approaches, our research aims to uncover hidden relationships and the evolutionary characteristics of solar flares and their source regions. Our previously proposed Sliding Window Multivariate Time Series Forest (Slim-TSF) has shown the feasibility of usage applied on multivariate time series data. A significant aspect of this study is the comparative analysis of our updated Slim-TSF framework against the original model outcomes. Preliminary findings indicate a notable improvement, with an average increase of 5\% in both the True Skill Statistic (TSS) and Heidke Skill Score (HSS). This enhancement not only underscores the effectiveness of our refined methodology but also suggests that our systematic evaluation and feature selection approach can significantly advance the predictive accuracy of solar flare forecasting models.

Researchers have been persistently working to address the issue of missing values in time series data. Numerous models have been proposed, striving to estimate the distribution of the data. The Radial Basis Functions Neural Network (RBFNN) has recently exhibited exceptional performance in estimating data distribution. In this paper, we propose a time series imputation model based on RBFNN. Our imputation model learns local information from timestamps to create a continuous function. Additionally, we incorporate time gaps to facilitate learning information considering the missing terms of missing values. We name this model the Missing Imputation Multivariate RBFNN (MIM-RBFNN). However, MIM-RBFNN relies on a local information-based learning approach, which presents difficulties in utilizing temporal information. Therefore, we propose an extension called the Missing Value Imputation Recurrent Neural Network with Continuous Function (MIRNN-CF) using the continuous function generated by MIM-RBFNN. We evaluate the performance using two real-world datasets with non-random missing and random missing patterns, and conduct an ablation study comparing MIM-RBFNN and MIRNN-CF.

This paper presents an extensive empirical study on the integration of dimensionality reduction techniques with advanced unsupervised time series anomaly detection models, focusing on the MUTANT and Anomaly-Transformer models. The study involves a comprehensive evaluation across three different datasets: MSL, SMAP, and SWaT. Each dataset poses unique challenges, allowing for a robust assessment of the models' capabilities in varied contexts. The dimensionality reduction techniques examined include PCA, UMAP, Random Projection, and t-SNE, each offering distinct advantages in simplifying high-dimensional data. Our findings reveal that dimensionality reduction not only aids in reducing computational complexity but also significantly enhances anomaly detection performance in certain scenarios. Moreover, a remarkable reduction in training times was observed, with reductions by approximately 300\% and 650\% when dimensionality was halved and minimized to the lowest dimensions, respectively. This efficiency gain underscores the dual benefit of dimensionality reduction in both performance enhancement and operational efficiency. The MUTANT model exhibits notable adaptability, especially with UMAP reduction, while the Anomaly-Transformer demonstrates versatility across various reduction techniques. These insights provide a deeper understanding of the synergistic effects of dimensionality reduction and anomaly detection, contributing valuable perspectives to the field of time series analysis. The study underscores the importance of selecting appropriate dimensionality reduction strategies based on specific model requirements and dataset characteristics, paving the way for more efficient, accurate, and scalable solutions in anomaly detection.

Over the past few decades, many applications of physics-based simulations and data-driven techniques (including machine learning and deep learning) have emerged to analyze and predict solar flares. These approaches are pivotal in understanding the dynamics of solar flares, primarily aiming to forecast these events and minimize potential risks they may pose to Earth. Although current methods have made significant progress, there are still limitations to these data-driven approaches. One prominent drawback is the lack of consideration for the temporal evolution characteristics in the active regions from which these flares originate. This oversight hinders the ability of these methods to grasp the relationships between high-dimensional active region features, thereby limiting their usability in operations. This study centers on the development of interpretable classifiers for multivariate time series and the demonstration of a novel feature ranking method with sliding window-based sub-interval ranking. The primary contribution of our work is to bridge the gap between complex, less understandable black-box models used for high-dimensional data and the exploration of relevant sub-intervals from multivariate time series, specifically in the context of solar flare forecasting. Our findings demonstrate that our sliding-window time series forest classifier performs effectively in solar flare prediction (with a True Skill Statistic of over 85\%) while also pinpointing the most crucial features and sub-intervals for a given learning task.

The detection of anomalies in multivariate time series data is crucial for various practical applications, including smart power grids, traffic flow forecasting, and industrial process control. However, real-world time series data is usually not well-structured, posting significant challenges to existing approaches: (1) The existence of missing values in multivariate time series data along variable and time dimensions hinders the effective modeling of interwoven spatial and temporal dependencies, resulting in important patterns being overlooked during model training; (2) Anomaly scoring with irregularly-sampled observations is less explored, making it difficult to use existing detectors for multivariate series without fully-observed values. In this work, we introduce a novel framework called GST-Pro, which utilizes a graph spatiotemporal process and anomaly scorer to tackle the aforementioned challenges in detecting anomalies on irregularly-sampled multivariate time series. Our approach comprises two main components. First, we propose a graph spatiotemporal process based on neural controlled differential equations. This process enables effective modeling of multivariate time series from both spatial and temporal perspectives, even when the data contains missing values. Second, we present a novel distribution-based anomaly scoring mechanism that alleviates the reliance on complete uniform observations. By analyzing the predictions of the graph spatiotemporal process, our approach allows anomalies to be easily detected. Our experimental results show that the GST-Pro method can effectively detect anomalies in time series data and outperforms state-of-the-art methods, regardless of whether there are missing values present in the data. Our code is available: https://github.com/huankoh/GST-Pro.

Many multivariate time series anomaly detection frameworks have been proposed and widely applied. However, most of these frameworks do not consider intrinsic relationships between variables in multivariate time series data, thus ignoring the causal relationship among variables and degrading anomaly detection performance. This work proposes a novel framework called CGAD, an entropy Causal Graph for multivariate time series Anomaly Detection. CGAD utilizes transfer entropy to construct graph structures that unveil the underlying causal relationships among time series data. Weighted graph convolutional networks combined with causal convolutions are employed to model both the causal graph structures and the temporal patterns within multivariate time series data. Furthermore, CGAD applies anomaly scoring, leveraging median absolute deviation-based normalization to improve the robustness of the anomaly identification process. Extensive experiments demonstrate that CGAD outperforms state-of-the-art methods on real-world datasets with a 15% average improvement based on three different multivariate time series anomaly detection metrics.

The loss function of Generative adversarial network(GAN) is an important factor that affects the quality and diversity of the generated samples for anomaly detection. In this paper, we propose an unsupervised multiple time series anomaly detection algorithm based on the GAN with message importance measure(MIM-GAN). In particular, the time series data is divided into subsequences using a sliding window. Then a generator and a discriminator designed based on the Long Short-Term Memory (LSTM) are employed to capture the temporal correlations of the time series data. To avoid the local optimal solution of loss function and the model collapse, we introduce an exponential information measure into the loss function of GAN. Additionally, a discriminant reconstruction score consisting on discrimination and reconstruction loss is taken into account. The global optimal solution for the loss function is derived and the model collapse is proved to be avoided in our proposed MIM-GAN-based anomaly detection algorithm. Experimental results show that the proposed MIM-GAN-based anomaly detection algorithm has superior performance in terms of precision, recall, and F1 score.

Multivariate time series data for real-world applications typically contain a significant amount of missing values. The dominant approach for classification with such missing values is to impute them heuristically with specific values (zero, mean, values of adjacent time-steps) or learnable parameters. However, these simple strategies do not take the data generative process into account, and more importantly, do not effectively capture the uncertainty in prediction due to the multiple possibilities for the missing values. In this paper, we propose a novel probabilistic framework for classification with multivariate time series data with missing values. Our model consists of two parts; a deep generative model for missing value imputation and a classifier. Extending the existing deep generative models to better capture structures of time-series data, our deep generative model part is trained to impute the missing values in multiple plausible ways, effectively modeling the uncertainty of the imputation. The classifier part takes the time series data along with the imputed missing values and classifies signals, and is trained to capture the predictive uncertainty due to the multiple possibilities of imputations. Importantly, we show that na\"ively combining the generative model and the classifier could result in trivial solutions where the generative model does not produce meaningful imputations. To resolve this, we present a novel regularization technique that can promote the model to produce useful imputation values that help classification. Through extensive experiments on real-world time series data with missing values, we demonstrate the effectiveness of our method.