Dependency Anomaly Detection for Heterogeneous Time Series: A Granger-Lasso Approach

The special characteristics of time series data, such as their high dimensionality and complex dependencies between variables make the problem of detecting anomalies in time series very challenging. Anomalies and more precisely dependency anomalies ensue from the temporal causal depen-dencies. Furthermore the graphical Granger causal models provide an appropriate environment to capture all the temporal dependencies in Gaussian time series. However many production systems are characterized by a high degree of complex stochastic processes consisting of heterogeneous time series. Considering this situation discovery of dependency anomalies would be more challenging since almost all the current algorithms are dealing with the homogeneous cases. Granger-Lasso algorithm is a well-known L1 penalization algorithm which copes with the temporal causality detection only for Gaussian time series. Inspired by this algorithm and considering the incremental heterogeneous time series generated in many different industries, we propose a modification for Granger-Lasso algorithm in the sense that it would be applicable for a larger class of heterogeneous time series. To introduce this algorithm we are motivated by generalized linear models. Moreover based on the proposed algorithm for discovery temporal dependencies we introduce its application in anomaly detection considering time series followed by distributions from exponential family, e.g. Poisson, binomial or multinomial distribution. The Granger-Lasso procedure is solved by using least square cost function with Lasso penalty for appropriately transformed input time series. The experimental results illustrate the performance and efficiency of the proposed algorithm on the synthetic and other datasets. We evaluated the proposed method on causality testing on different examples.