# Improving Re-Identification by Estimating and Utilizing Diverse Uncertainty Types for Embeddings
## 4 Experiments
### Simple Score-Level Fusion
#### 4.3.4 Utilizing the Estimated Model Uncertainty to Adjust Feature Vectors
Our hyperparameter search experiments show that while the best values for \(c\) deviate strongly for different trained models, they do not deviate as much if we use \(\lambda\). The best value for \(\lambda\) is approximately half the dimensionality of the uncertainty vector \(\frac{d}{2}\). Using \(\lambda=\frac{d}{2}\), we can now compute an individual \(c\) for each input. Table 5 shows that applying this function to each input produces almost identical performance compared to the best results achieved with a constant \(c\). \begin{table}
\begin{tabular}{l c c} \hline \hline
**Distance Matrix** & **mAP [\%]** & **rank-1 [\%]** \\ \hline BOT baseline [66] & \(86.41\pm 0.09\) & \(94.42\pm 0.23\) \\ \(D^{\mu}\) (identical to UAL [25]) & \(86.77\pm 0.14\) & \(94.64\pm 0.21\) \\ \hline \(D^{\mu,\Sigma^{(M)}},c=0.1225\) & \(87.21\pm 0.17\) & \(94.70\pm 0.17\) \\ \(D^{\mu,\
abla^{(M)}},c=0.2435\) & \(87.20\pm 0.17\) & \(94.70\pm 0.21\) \\ \hline \(D^{\mu,\Sigma^{(  
With the approximation \(\lambda=\frac{d}{2}\) and the application of Equation (47) for each input, we got almost identical results while removing the need for a hyperparameter search. We are now able to use the estimated model uncertainty to adjust the feature vector in a straightforward way. Conclusion on the Utilization of Uncertainties  
Data uncertainty is already utilized in our architecture to divide the result of the mean head by the result of the variance head, as in the UAL approach [25]. We showed that the estimated _model uncertainty_ vector can be utilized to further adjust the feature vector. The estimated distributional uncertainty is very helpful for identifying out-of-distribution data, which is explained in more detail in Section 4.4. Additionally, the estimated distributional uncertainty can be utilized to derive a scalar value to further improve the ReID performance, but only marginally, as explained below. Further Investigations  
To verify that our derived formula is a good way to estimate the hyperparameter \(c\), we also experimented with a wide variety of possibilities. We examined the three types of uncertainties as the basis for the computation of a constant \(c\), both as standard deviation and as variance. We derived a scalar value by applying the inverse of the \(\mathrm{l}_{1}\)-norm of the logarithm \(((\|\ln(\cdot)\|_{1})^{-1})\), the inverse of the \(\mathrm{l}_{1}\)-norm \(((\|\cdot\|_{1})^{-1})\), the entropy \((\mathcal{H}(\cdot))\), and the vector length \((\|\cdot\|_{2})\). For each of these scalar values, we performed a hyperparameter search to find an adequate multiplication factor \(\lambda\). Furthermore, instead of the model uncertainty we also employed the other uncertainty types, both as standard deviation and as variance, to refine the feature vector as explained above. Overall, we checked 150 variations, each optimized via hyperparameter search. None of these variants improved the performance noticeably over the approach described above. The best result is achieved by applying the inverse of the \(\mathrm{l}_{1}\)-norm of the distributional uncertainty estimate as variance, and to refine the feature vector with the model uncertainty estimate as variance and the derived scalar constant. However, this result (mAP \([\%]=87.213\pm 0.170\)) is only 0.007 percentage points better than the result when employing Equation (47) (\(87.206\pm 0.178\)). Therefore, it can be considered approximately equal. Nevertheless, the result described here, represents the best result achieved by our approach UBER in this paper. Therefore, this result is also shown in Table 1 and Figure 5 to compare with the state of the art. Specifically in Figure 5, we can see the significant improvement over UAL [25], which served as the basis for our network architecture. Using the entropy, the inverse of the \(\mathrm{l}_{1}\)-norm of the logarithm, or the inverse of the \(\mathrm{l}_{1}\)-norm of any of the uncertainty types to derive the scalar value also achieved good results.