# Improving Re-Identification by Estimating and Utilizing Diverse Uncertainty Types for Embeddings
## 4 Experiments
### Experimental Validation of the Distributional Uncertainty Estimate
#### 4.4.3 Uncertainty Score Distributions When Controlling for Another Uncertainty Type
uncertainty score distributions of the reduced sets (Q), (D1)-(D4)\({}^{\mathcal{IH}(\Sigma^{(D)})}\) in Figure 8e are very similar to the distributional uncertainty score distributions of the original sets (Q), (D1)-(D4) in Figure 8c. The means of the distributions of the sets (Q), (D1)-(D4)\({}^{\mathcal{IH}(\Sigma^{(D)})}\) remain in the correct order. The distractor set (D1)\({}^{\mathcal{IH}(\Sigma^{(D)})}\) still largely overlaps with the in-distribution set (Q)\({}^{\mathcal{IH}(\Sigma^{(D)})}\) for the previously described reasons. The distractor sets (D2)-(D4)\({}^{\mathcal{IH}(\Sigma^{(D)})}\) with a higher OOD degree share only a small overlap with the in-distribution set (Q)\({}^{\mathcal{IH}(\Sigma^{(D)})}\). The mean of the distributions of the two distractor sets (D3)\({}^{\mathcal{IH}(\Sigma^{(D)})}\) and (D4)\({}^{\mathcal{IH}(\Sigma^{(D)})}\) with the highest OOD degree move slightly closer to the in-distribution set (Q)\({}^{\mathcal{IH}(\Sigma^{(D)})}\). Based on Figure 4d, this can be attributed to the fact that the samples in the original sets (D3) and (D4) with the highest estimated distributional uncertainty also have an estimated data uncertainty score higher than the threshold \(\tau_{{}^{\mathcal{IH}}\mathcal{H}(\Sigma^{(D)})}\). We essentially observe what we expected from the mathematical theory. The distributional uncertainty score distributions are barely affected by filtering based on low estimated data uncertainty. The distributional uncertainty estimate is still able to predict the OOD degree. Therefore, this observation gives strong support to our hypothesis that our estimate of distributional uncertainty is a much better fit than the data uncertainty estimate for predicting the OOD degree. Furthermore, the alignment of the observation and the mathematical theory supports our hypothesis that the proposed extraction of distributional uncertainty as variance of the learned variance vector is a mathematically grounded distributional uncertainty estimate. In case of low estimated distributional uncertainty, we saw very sharp distributions of the data uncertainty scores for all the sets. Below, we investigate how the data uncertainty estimate behaves in case of high estimated distributional uncertainty. Based on the mathematical theory, in this case, we expect the data uncertainty score distributions to be very wide since the model's ability to accurately predict the data uncertainty is expected to be reduced under the condition of high distributional uncertainty. If we verify this, it would imply that we should not trust the data uncertainty estimate in this situation. Again, we first filter the sets before computing the distributions. This time, we use only the samples of the sets (Q), (D1)-(D4) that had a high distributional uncertainty score in Figure 8c. As criteria, we use a distance of 3 standard deviations with respect to the query set (Q) to the mean of the query set (Q), as defined in Equation (51). \[\mathcal{H}\Big{(}\Sigma^{(V)}\Big{)}>\mathbb{E}\Big{\{}\mathcal{H}\Big{(} \Sigma^{(V),\mathcal{Q}}_{i}\Big{)}\Big{\}}_{i=1}^{Q}+3\cdot\sqrt{\forall \text{ar}\Big{\{}\mathcal{H}\Big{(}\Sigma^{(V),\mathcal{Q}}_{i}\Big{)}\Big{\}} _{i=1}^{Q}} \tag{51}\]  
Therefore, the threshold for filtering the sets is \(\tau_{{}^{\mathcal{IH}}\mathcal{H}(\Sigma^{(V)})}=-5794\). The remaining number of images in each set, along with the percentage of the original set size that remains, is provided in Table 11.  
In all sets, at least 26 images remain. Therefore, we can display the distributions for all sets. Figure 8f shows the distributions of the reduced sets.