# Contextual Background Estimation for Explainable AI in Temperature Prediction
## 3 Results
### Evaluation of Background Estimation Method
Although each distribution shows relatively minor fluctuations, since they belong to the same feature, they exhibit a wide range and large fluctuations. A similar situation can be observed in Figure 9 on the right side, where the percentage assigned to each feature is divided into three distributions. This strongly suggests that there are several types or clusters of sequences that can be used  
Figure 8: Dispersion of percentage of explanation for each feature that has mean percentage equal to or larger than 2% for stations 352200375 and 353200272. Figure 10: Utility of each feature of IMGW stations. Figure 9: Dispersion of percentage of explanation for each feature that has mean percentage equal to or larger than 2% for stations 352140310 and 352150300.  
as backgrounds. Whenever possible, these should be treated separately, and the user should decide which type of sequence to use. This is a key difference from the previous method. Previously, it would not have been possible to distinguish these clusters, but they are now clearly visible. In the previous method, all the sequences would have been combined and averaged. This also explains why the previous method, while fast and providing rough estimations of explanations across the entire dataset, is less effective. A difficult and cumbersome situation is presented in Figure 9 on the left. The range of the feature \"Pressure at station level\" is large, and there are no means of modifying the backgrounds to limit these fluctuations. This highlights the need to identify challenging features that can introduce uncertainty in explanations. Such features can be identified using the utility index. The utility index indicates whether a feature can be reliably used to explain the model's behavior and whether we can trust the explanations. If the results do not highlight features that can effectively explain most of the prediction, further analysis is required to reduce fluctuations. For instance, clustering the backgrounds and dividing the set of backgrounds into more precise subsets may better represent the context. The utility indices are presented in Figure 10.  
The utility indices for the stations discussed above can be verified. In the case of station 353200272, for which the explanations were visibly stable, high utility values are notable. Air temperature has a much higher utility value, even though it does not explain as much as \"Pressure at station level\". However, it has a significantly lower standard deviation, and, as a result, it was rewarded for its stability. On the other hand, the explanations for station 352150300 are extremely unstable, and, therefore, each feature has a low utility value. The steam pressure for this station has a high mean importance of 41% but also a large standard deviation of 5%. At the same time, wind gusts demonstrate a very low standard deviation of 0.10% but also an insignificantly low share of explanation. The utility values for this station are low because there are several distributions within each feature. Further analysis could help to distinguish these distributions and create groups of stable backgrounds. In the case of station 352140310, steam pressure and air temperature both have comparable percentages of explanation and similar standard deviations, which is why they were assigned similar utility values. Utility indices are valid only for a given set of backgrounds, so they cannot be used to draw conclusions about the entire dataset or all the possible backgrounds. Additionally, they do not provide further insights into the behavior of the model beyond the particular prediction \(y_{e}\) and the corresponding \(y_{b}\). Utility could be calculated for the entire dataset, similarly to in the Mean Background Method, to observe how it changes across the dataset. This could provide an impression of stability over the entire dataset. However, the main focus of this article is to study local importance.