# 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

Table 9: Statistics for subsets of images with low distributional uncertainty (\(\downarrow\mathcal{H}(\Sigma^{(V)})\)). that have a higher data uncertainty score. The distractor sets (D2)\({}^{\mathcal{H}(\Sigma^{(V)})}\) and (D3)\({}^{\mathcal{H}(\Sigma^{(V)})}\) with slightly higher OOD degree still share a large overlap with the in-distribution set (Q)\({}^{\mathcal{H}(\Sigma^{(V)})}\). The two samples of the distractor set (D4)\({}^{\mathcal{H}(\Sigma^{(V)})}\) with the highest OOD degree also fall within the overlapping area of the in-distribution set (Q)\({}^{\mathcal{H}(\Sigma^{(V)})}\). Even though the means of the distributions of the sets remain in the correct order, the large overlap between the distributions of the in-distribution set (Q)\({}^{\mathcal{H}(\Sigma^{(V)})}\) and the distractor sets (D1)-(D4)\({}^{\mathcal{H}(\Sigma^{(V)})}\) shows that the data uncertainty estimate is not very useful for distinguishing the in-distribution set (Q)\({}^{\mathcal{H}(\Sigma^{(V)})}\) and the distractor sets (D1)-(D4)\({}^{\mathcal{H}(\Sigma^{(V)})}\) in case of low distributional uncertainty. The reason that the data uncertainty estimate is still able to order the sets correctly to a certain extent can be attributed to three factors: (1) measurement errors and image corruptions, which contribute to both kinds of uncertainty; (2) labeling errors stemming from the ambiguous nature of the sets; and (3) the high correlation between data and distributional uncertainty, as discussed in Section 4.2. Now, we investigate whether there are similar results for the distributional uncertainty score distributions when considering images with low data uncertainty scores. From Figure 4d, we can already observe that this is likely not the case. Instead, in case of low estimated data uncertainty, the ability of the distributional uncertainty estimate to differentiate the in-distribution set (Q) and the distractor sets (D1)-(D4) should not be affected. Moreover, also based on the mathematical theory where only data uncertainty is conditioned on distributional uncertainty and not the other way around, the distributional uncertainty score distributions of the sets should not be affected in case of low data uncertainty. Similarly to the previous experiment, 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 low data uncertainty score in Figure 8b. As criteria, we use a distance of 1.5 standard deviations with respect to the query set (Q) to the mean of the query set (Q), as defined in Equation (50). \[\mathcal{H}\Big{(}\Sigma^{(D)}\Big{)}<\mathbb{E}\Big{\{}\mathcal{H}\Big{(} \Sigma^{(D),\mathcal{Q}}_{i}\Big{)}\Big{\}}_{i=1}^{Q}+1.5\cdot\sqrt{\mathbb{ Var}\Big{\{}\mathcal{H}\Big{(}\Sigma^{(D),\mathcal{Q}}_{i}\Big{)}\Big{\}}_{i=1}^{Q}} \tag{50}\]  
Therefore, the threshold for filtering the sets is \(\tau_{\mathcal{H}(\Sigma^{(D)})}=2705\). The remaining number of images in each set, along with the percentage of the original set size that remains, is provided in Table 10.  
In all sets, at least 30 images remain. Therefore, we can display the distributions for all sets. Figure 8e shows the distributions of the reduced sets. As expected, the distributional \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Set** & & **\# of Images** & **Remaining** \\ \hline Query & (Q)\({}^{\mathcal{H}(\Sigma^{(D)})}\) & 3110 & 92.3\% \\ Full Human & (D1)\({}^{\mathcal{H}(\Sigma^{(D)})}\) & 204 & 73.4\% \\ Human Fragments & (D2)\({}^{\mathcal{H}(\Sigma^{(D)})}\) & 825 & 47.7\% \\ Objects & (D3)\({}^{\mathcal{H}(\Sigma^{(D)})}\) & 110 & 19.4\% \\ Background/Blur & (D4)\({}^{\mathcal{H}(\Sigma^{(D)})}\) & 30 & 13.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistics for subsets of images with low data uncertainty (\(\mathcal{H}(\Sigma^{(D)})\)).