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Causal analysis based on non-uniform embedding schemes is an important way to detect the underlying interactions between dynamic systems. However, there are still some obstacles to estimating high-dimensional conditional mutual information and forming optimal mixed embedding vector in traditional non-uniform embedding schemes. In this study, we present a new non-uniform embedding method framed in information theory to detect causality for multivariate time series, named LM-PMIME, which integrates the low-dimensional approximation of conditional mutual information and the mixed search strategy for the construction of the mixed embedding vector. We apply the proposed method to simulations of linear stochastic, nonlinear stochastic, and chaotic systems, demonstrating its superiority over partial conditional mutual information from mixed embedding (PMIME) method. Moreover, the proposed method works well for multivariate time series with weak coupling strengths, especially for chaotic systems. In the actual application, we show its applicability to epilepsy multichannel electrocorticographic recordings. [ABSTRACT FROM AUTHOR]

We address the problem of unsupervised anomaly detection for multivariate data. Traditional machine learning based anomaly detection algorithms rely on specific assumptions of normal patterns and fail to model complex feature interactions and relations. Recently, existing deep learning based methods are promising for extracting representations from complex features. These methods train an auxiliary task, e.g., reconstruction and prediction, on normal samples. They further assume that anomalies fail to perform well on the auxiliary task since they are never trained during the model optimization. However, the assumption does not always hold in practice. Deep models may also perform the auxiliary task well on anomalous samples, leading to the failure detection of anomalies. To effectively detect anomalies for multivariate data, this paper introduces a teacher-student distillation based framework Distillated Teacher-Student Network Ensemble (DTSNE). The paradigm of the teacher-student distillation is able to deal with high-dimensional complex features. In addition, an ensemble of student networks provides a better capability to avoid generalizing the auxiliary task performance on anomalous samples. To validate the effectiveness of our model, we conduct extensive experiments on real-world datasets. Experimental results show superior performance of DTSNE over competing methods. Analysis and discussion towards the behavior of our model are also provided in the experiment section. [ABSTRACT FROM AUTHOR]