# 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  
Since our results regarding the prediction of the OOD degree by utilizing the data uncertainty estimate were somewhat inconclusive, in the following, we conduct further investigations. First, we examine the estimated data uncertainty for subsets of images for which low distributional uncertainty was estimated. Furthermore, we also examine the estimated distributional uncertainty for subsets of images for which low data uncertainty was estimated. This is intended to confirm that, as suggested by the mathematical model (Equation (2)), the dependency between data uncertainty and distributional uncertainty is unidirectional. Additionally, we examine the estimated data uncertainty for subsets of images for which high distributional uncertainty was estimated. This serves to verify the derivation from the mathematical model that given high distributional uncertainty, the data uncertainty estimate becomes unreliable. As discussed in Section 3.1.2, we should not trust the data uncertainty estimate in case of high distributional uncertainty. For this reason, we investigate the data uncertainty score distribution of images with low distributional uncertainty scores. Based on the mathematical theory, we expect that in case of low distributional uncertainty, the width of the data uncertainty score distributions should be small for all sets (Q), (D1)-(D4). Furthermore, we expect that a low distributional uncertainty score indicates a low OOD degree. Therefore, the ability of data uncertainty to appropriately order and separate the distractor sets should be strongly diminished. In contrast to the previous experiments, we now do not compute the distributions on the entire sets (Q), (D1)-(D4), but instead filter the sets. First, we examine data uncertainty in case of low distributional uncertainty. Therefore, we use only the samples of the sets (Q), (D1)-(D4) that had a low distributional uncertainty score in Figure 5c. 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 (49). \[\mathcal{H}\Big{(}\Sigma^{(V)}\Big{)}<\mathbb{E}\Big{\{}\mathcal{H}\Big{(} \Sigma^{(V),\mathcal{Q}}\Big{)}\Big{\}}_{i=1}^{Q}+1.5\cdot\sqrt{\mathbb{Var} \Big{\{}\mathcal{H}\Big{(}\Sigma^{(V),\mathcal{Q}}_{i}\Big{)}\Big{\}}_{i=1}^{Q}} \tag{49}\]  
Therefore, the threshold for filtering the sets is \(\tau_{\downarrow\mathcal{H}\big{(}\Sigma^{(V)}\big{)}}=-6069\). The remaining number of images in each set, along with the percentage of the original set size that remains, is provided in Table 9.  
We can see, that only two images of the distractor set (D4) with the highest OOD degree remain. Similarly, only 31 images remain of the distractor set (D3) with the second-highest OOD degree. Figure 7(d) shows the distributions of the reduced sets. Since the distractor set (D4)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\) contains only 2 samples, their uncertainty values are plotted instead of a distribution. We observe that the sets are still ordered correctly by the data uncertainty estimate. However, the distributions for the different sets share a large overlap. The distractor set (D1)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\) almost perfectly overlays the in-distribution set (Q)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\), with only some exceptions \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Set** & & **\# of Images** & **Remaining** \\ \hline Query & (Q)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\) & 3119 & 92.6\% \\ Full Human & (D1)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\) & 199 & 71.6\% \\ Human Fragments & (D2)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\) & 304 & 17.6\% \\ Objects & (D3)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\) & 31 & 5.5\% \\ Background/Blur & (D4)\({}^{\downarrow\mathcal{H}(\Sigma^{(V)})}\) & 2 & 0.9\% \\ \hline \hline \end{tabular}
\end{table}