# Improving Re-Identification by Estimating and Utilizing Diverse Uncertainty Types for Embeddings
## 4 Experiments
### Analysis of Correlation between Uncertainty Types  
In this section, we examine the degree of independence between the three types of estimated uncertainty. This should determine whether the uncertainty types are correlated, if they are conditioned upon each other, or whether they are independent due to the extraction at different positions in the neural network. If the latter were to be the case, this would be in contradiction with the assumption that the estimated uncertainties follow mathematical theory. In accordance with mathematical theory, we expect that two types of uncertainty estimates will be correlated to some degree if the term of one type of uncertainty in Equation (2) is conditioned upon the term of another uncertainty type. From Equation (2), we know that the distributional uncertainty term is conditioned upon the model uncertainty term, and the data uncertainty term is conditioned upon the distributional uncertainty term. Therefore, we expect that a correlation will be observed between the model uncertainty estimate and the distributional uncertainty estimate. Furthermore, we also expect that the data uncertainty estimate and the distributional uncertainty estimate will be correlated to some degree. Conversely, we expect only a low correlation between the model uncertainty estimate and the data uncertainty estimate.  
In order to investigate these relationships, it is necessary to compare the three types of uncertainties for identical inputs. Accordingly, for the three types of uncertainties, we extracted estimated uncertainty vectors for the query and gallery partitions of the Market-1501 dataset [68]. Then, we derived scalar uncertainty values from the estimated uncertainty vectors by computing the entropy, as discussed in Section 3.3.6. Figure 4a-c shows pairwise joint distributions for each pair of uncertainty types. Furthermore, a linear fit was applied to each plot to generate a trend line, and the respective correlation is reported in the plots. The visualized contour lines of the joint distribution are generated using Kernel Density Estimation (KDE).  
Additionally, Figure 4d shows the contour lines for different subsets of the Market-1501 dataset. The separability of these in-distribution and out-of-distribution sets by utilizing either data uncertainty or distributional uncertainty is investigated in Section 4.4.  
As expected, Figure 4a illustrates that the model uncertainty estimate and the data uncertainty estimate only have a very low correlation. Furthermore, the outcome of the comparison between the distributional uncertainty estimate and the data uncertainty estimate, as illustrated in Figure 4b, aligns with our expectations. The same is true for the results of the comparison of the distributional uncertainty estimate and the data uncertainty estimate, as illustrated in Figure 4c. The correlation between the distributional uncertainty estimate and the data uncertainty estimate is 0.7485, while the correlation between the distributional uncertainty estimate and the model uncertainty estimate is 0.6938. Given that both correlation coefficients are around 0.7 or more, we can consider these pairs of uncertainty estimates to be highly correlated. Therefore, the results of the pairwise correlation analyses for the three types of estimated uncertainty provide support for the hypothesis that the estimated uncertainties are in accordance with the mathematical theory.