# An Attention-Based Deep Convolution Network for Mining Airport Delay Propagation Causality
## 3 Methodology  
### Method Overview  
The general definition of causality contains the following two characteristics [45]: (a) temporal precedence: the cause occurs before and the effect occurs after, and the chronological order of cause and effect cannot be reversed; (b) physical influence: changing the cause will affect the result, that is, the change in the result caused by the state change in the cause is objective. In view of the characteristic of time sequence, it is easier to take it into account when constructing the causal relationship mining of airport delay propagation based on time series. For example, when constructing the input and output of the model, the delay status information of the \"cause\" airport and \"effect\" airport is used as input and output, respectively, but the delay status information of the \"effect\" airport is later than that of \"cause\" airport. The difficulty with causality discovery is how to take physical effects into account when building a model.  
For the causal discovery of airport delay propagation, the mainstream mining algorithms are divided into two stages: prediction and causality analysis [15; 31]. In the first stage, a model that uses the delay time series of the \"cause\" airport to predict the delay of the \"effect\" airport is built. However, historical and current delays at one airport help predict future delays at another airport, and there may be a correlation. Therefore, in the second stage, it is necessary to use some criteria to judge the true causal relationship between the airport pairs based on the prediction model. Like the mainstream causality mining algorithm, this paper adopts a two-stage mining idea, as shown in Figure 4. The difference from the existing mainstream methods is that because the airport is a dynamic and complex network, this section builds a model directly from the perspective of the airport network, and establishes a deep temporal convolution network (DTCN) airport delay prediction model. The model takes the delay time series of all airports as model input, which can better capture the interaction between airports. In order to measure the degree of influence of all airports on the target airport, an attention mechanism is introduced into the model, and the degree of influence is quantitatively measured by attention parameters.  
Figure 3: Diagram of confounding causality. Airport A, airport B, and airport C are the “cause” airports of airport Z.  
In general, the attention parameter measures the strength of the delay correlation between two airports. A large value of the attention parameter indicates a strong correlation; conversely, a small value of the attention parameter indicates a weak correlation. Therefore, when causality is performed in the second stage, the airport pairs with weak correlation are first eliminated according to the value of the attention parameter. On this basis, a candidate causality screening based on attention score is proposed, and the airport pairs with strong correlation are reserved as the candidate causality set. Since the temporal order between airport pairs has been considered in the first stage, in order to judge whether the causal relationship pairs in the candidate causal relationship set are true causal relationships, a true causality verification based on a \(t\)-test is proposed. By intervening on delays at \"cause\" airports, the time series of \"cause\" airports are randomly permuted and fed into the learned prediction model. The \(t\)-test method is used to judge the significance level of the \"effect\" airport prediction error before and after the sequence rearrangement, and further according to the significance level to judge whether it belongs to the real causal relationship, and finally the airport delay propagation causal relationship set is obtained. Finally, we propose a direct causality verification method based on time-lapse analysis to distinguish direct causality from indirect causality.