## 2 Related Work
### Time Series Causal Network  
Telemetry data is essentially a multivariate time series with complex causality among its multiple parameters. Causality is more interpretable than correlation. Correlation only means \"synchronized changes\" of two variables, not directional, but causality means that a change in one variable will irreversibly affect another variable in some fixed pattern. Causality reflects not only the correlation in the aspect of statistics, but also the mutual influence in terms of physical mechanism or logic. Causality has been widely applied in many areas such as physics [14], biomedical science [15], ecosystems [16], and neuroscience [17].  
Causal Bayesian Network (CBN) [18] represents a form of a time series causal network, and it is a specific version of Bayesian networks. A Bayesian network is based on the principles of Bayesian statistics, it is suitable for expressing and analyzing uncertain and probabilistic events. A Bayesian network uses the conditional probability to express the strength of the relationship, and uses the prior probability to express the information without a parent node. CBN is a Bayesian network that further stipulates that the edge between nodes indicates the causal relationship between two variables, the out-degree node of the edge denotes the cause variable (usually called source variable), and the in-degree node of the edge denotes the result variable (usually called the target variable).  
A time series causal network is a causal network that considers the causal relationship and time lag between variables. The Directed Acyclic Graph (DAG) \(\mathbf{G}=\{\mathbf{X},\mathbf{E},\mathbf{T}\}\) denotes the time series causal network, and the node set \(\mathbf{X}=\{X^{1},X^{2},...,X^{n}\}\) denotes the set of variables. These variables are supposed to all be observable [19]. The set of directed edges \(\mathbf{E}\) denotes the causal relationship between nodes, and the causal time lag \(\mathbf{T}=\{\tau_{1},\tau_{2},...,\tau_{n}\}\) denotes the max time lags of causal relationships. Figure 2 shows an example of a time series causal network.  
Figure 2: An example of a time series causal network with five nodes and five edges. The arrows denote causal links, and \(\tau_{max}\) denotes the max time lag of each causality.  
Time series causal inference algorithms include methods based on regression analysis, methods based on information theory, and methods based on state space model [20]. Methods based on information theory can be applied to high-dimensional data as well as measuring the strength of the causality. Thus, they are widely used in time series causal inference. [PERSON] et al. [21] proposed Binary Transfer Entropy (BTE) as a measure for causality strength. BTE can be used for non-linear data, but not for multivariate time series. [PERSON] et al. [22] proposed Causal Entropy (CE) to measure causal strength. CE can be applied to multivariate time series and can also distinguish direct and indirect causality, but it cannot reflect the true causality strength. [PERSON] et al. [23] proposed Normalized Causal Entropy (NCE), which can eliminate the indirect influence between nodes and measure the strength of causality more accurately than traditional methods by unifying dimension. However, for time series with a large amount of variables, its calculation complexity is high and it depends on prior knowledge. [PERSON] [24] proposed the PCMCI (Peter Clark-Moment Conditional Independence) algorithm for constructing a causal network in a large scale multivariate time series. The algorithm is the improved version of the traditional PC (Peter Clark) algorithm. PCMCI removes false causality by adding an MCI test, but it has still not completely overcome the shortcomings of the PC algorithm, which has poor comprehensibility and robustness. Time series causal inference methods that are suitable for non-stationary, high-dimensional sequences, and can accurately reflect causal strength are the focus of current scholars.