# Improving Re-Identification by Estimating and Utilizing Diverse Uncertainty Types for Embeddings
## 4 Experiments
### Experimental Validation of the Distributional Uncertainty Estimate
#### 4.4.2 Analysis of Uncertainty Score Distributions
While this predictive ability seemingly contradicts the theoretical considerations, this may be due to the issue with its reliability in cases of high distributional uncertainty mentioned above. This is supported by the fact that the standard deviation of the data uncertainty score distributions generally increases with OOD degree, which is exactly what we expected from the mathematical model. While the distractor set (D1) with the lowest OOD degree does not quite fit this pattern, we can clearly see in Figure 8b that the main body of the distribution of (D1) does have a smaller standard deviation than that of the distractor set (D2), which has a slightly higher OOD degree. Furthermore, we can see that the unexpectedly high standard deviation of the distractor set (D1) is due to a smaller second mode in the distribution with images of higher data uncertainty scores. This is likely to be the part of the images in (D1) which show noticeably worse image quality compared to the others, which correctly is associated with a higher data uncertainty. Overall, we have some supporting and some unclear evidence in relation to the theoretical considerations. Therefore, we also examine the distributions of only those images with low distributional uncertainty, which should be free of the observed effect. This investigation is further discussed in Section 4.4.3. Since distributional uncertainty is precisely the type of uncertainty that measures the OOD degree, we would expect a clear ordering of the distributional uncertainty score distributions and a clear distinction between the in-distribution set (Q) and the OOD sets (D1)-(D4). However, the distractor set (D1) with the lowest OOD degree is still largely similar to the in-distribution set (Q) and contains those images that still contain enough information to make a confident prediction regarding the identity. Therefore, we expect the distribution of the distractor set (D1) to be quite similar to that of the in-distribution set (Q). Conversely, the distractor set (D4) with the highest OOD degree should have a clear distinction from the in-distribution set (Q), even if it does not necessarily have to be perfectly separable due to the ambiguous nature of many images, as discussed in Section 4.4.1. We can immediately see in Figure 8c and Table 7c that the means of the distributions are ordered by the OOD degree of the respective set. In Figure 8c and Table 8c, we can also compare the relative standard deviations of the distributions in terms of multiples of the standard deviation of the in-distribution set (Q) for the distractor sets (D1)-(D4). We observe that the relative standard deviations of the distributional uncertainty score distributions for the distractor sets (D1)-(D4) in Figure 8c and Table 8c are smaller than those of the data uncertainty score distributions for the distractor sets (D1)-(D4) in Figure 8b and Table 8b. Furthermore, we observe the same pattern of increase in standard deviation for an increase in OOD degree as for the data uncertainty score distributions, including the exception for the distractor set (D1). However, we observe much smaller relative standard deviations for the distributional uncertainty score distributions. This seems to indicate a confident prediction of distributional uncertainty that does not become more unreliable with increased OOD degree of the distractor sets. The degree of overlap between the in-distribution set (Q) and the distractor set (D1) with the lowest OOD degree is very high. Therefore, the distractor set (D1) is rather judged as an in-distribution set, which is plausible considering that a re-identification of the depicted individuals is still possible. The degree of overlap between the in-distribution set (Q) and the respective distractor sets (D2)-(D4) is smaller the higher the OOD degree is. Therefore, the distributional uncertainty estimate seems to be a good predictor of the OOD degree.