# 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
We can immediately see that the means of the distributions are not in the correct order. Furthermore, there exists a large overlap between the distributions of all sets. Surprisingly, some of the lowest model uncertainty values are observed for images in the distractor set (D4) with the highest OOD degree. It appears that the model uncertainty estimate is unsuited to predicting the OOD degree. This fits our expectations based on the mathematical theory of how a model uncertainty estimate should behave in this situation. Data Uncertainty Score Distribution  
The data uncertainty term \(p(z\,|\,\xi)\) in the mathematical model is separate from but not independent of the distributional uncertainty term \(p(\xi\,|\,x,\theta)\). Ideally, the data uncertainty score distributions would be indifferent to the OOD degree, as it is a separate quantity. However, the conditional dependence of the data uncertainty term on the distributional uncertainty term likely means that this is not the case. As we saw in Figure 1, the reliability of the data uncertainty estimate decreases with increasing distributional uncertainty. Therefore, images with higher distributional uncertainty should exhibit larger spread in data uncertainty estimates around their actual data uncertainty. As can be seen in Figure 8b and Table 7b, the means of the distributions are ordered by the OOD-degree of the respective set. In Figure 8b and Table 8b, we also observe that the uncertainty score distributions for the OOD sets exhibit standard deviations that are considerably higher than the one of the query set and are higher for greater OOD degree. Only the distractor set (D1) with the lowest OOD degree does not quite fit this pattern, since its standard deviation is larger than that of the distractor set (D2) with the slightly higher OOD degree. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Set** & & **(a)** & **(b)** & **(c)** & **(d)** & **(e)** & **(f)** \\ \hline Full Human & (D1) & 0.53 & 1.43 & 0.85 & 0.35 & 0.47 & 4.50 \\ Human Fragments & (D2) & 1.47 & 2.29 & 2.74 & 1.10 & 2.61 & 1.07 \\ Objects & (D3) & 1.41 & 4.55 & 3.93 & 1.34 & 3.07 & 2.80 \\ Background/Blur & (D4) & 0.38 & 6.57 & 4.57 & 1.97 & 3.69 & 4.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Number of standard deviations of the query score distribution that the mean of the uncertainty score distribution of the respective set is above the mean of the query score distribution for (**a**) model uncertainty, (**b**) data uncertainty, (**c**) distributional uncertainty, (**d**) data uncertainty in case of low distributional uncertainty, (**e**) distributional uncertainty in case of low data uncertainty, and (**f**) data uncertainty in case of high distributional uncertainty. For a visualization, we refer to Figure 8. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Set** & & **(a)** & **(b)** & **(c)** & **(d)** & **(e)** & **(f)** \\ \hline Full Human & (D1) & 1.08 & 2.92 & 1.50 & 1.49 & 1.13 & 2.60 \\ Human Fragments & (D2) & 1.28 & 2.55 & 1.33 & 1.66 & 1.21 & 2.59 \\ Objects & (D3) & 1.95 & 3.62 & 1.57 & 1.62 & 1.21 & 3.10 \\ Background/Blur & (D4) & 2.54 & 5.68 & 1.81 & 0.88 & 1.19 & 4.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Factor by which the standard deviation of the uncertainty score distribution for the respective set is larger than the standard deviation of the query score distribution for (**a**) model uncertainty, (**b**) data uncertainty, (**c**) distributional uncertainty, (**d**) data uncertainty in case of low distributional uncertainty, (**e**) distributional uncertainty in case of low data uncertainty, and (**f**) data uncertainty in case of high distributional uncertainty. For a visualization, we refer to Figure 8.  
The data uncertainty estimate appears to be somewhat suitable for predicting the OOD degree, though the large standard deviations and largely overlapping distributions make it less than ideal.