Entropy Causal Graphs for Multivariate Time Series Anomaly Detection

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

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Causal Discovery from Temporal Data: An Overview and New Perspectives

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing casual discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series casual discovery, and event sequence casual discovery. However, most previous surveys are only focused on the time series casual discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data casual discovery.Comment: 52 pages, 6 figure

Exploring Causal Learning through Graph Neural Networks: An In-depth Review

In machine learning, exploring data correlations to predict outcomes is a fundamental task. Recognizing causal relationships embedded within data is pivotal for a comprehensive understanding of system dynamics, the significance of which is paramount in data-driven decision-making processes. Beyond traditional methods, there has been a surge in the use of graph neural networks (GNNs) for causal learning, given their capabilities as universal data approximators. Thus, a thorough review of the advancements in causal learning using GNNs is both relevant and timely. To structure this review, we introduce a novel taxonomy that encompasses various state-of-the-art GNN methods employed in studying causality. GNNs are further categorized based on their applications in the causality domain. We further provide an exhaustive compilation of datasets integral to causal learning with GNNs to serve as a resource for practical study. This review also touches upon the application of causal learning across diverse sectors. We conclude the review with insights into potential challenges and promising avenues for future exploration in this rapidly evolving field of machine learning

Optimal model-free prediction from multivariate time series

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal pre-selection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used sub-optimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure

Optimal model-free prediction from multivariate time series

© 2015 American Physical Society.Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal preselection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used suboptimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Niño Southern Oscillation