# Improving Re-Identification by Estimating and Utilizing Diverse Uncertainty Types for Embeddings
## 4 Experiments
### Utilization of Model Uncertainty during Inference
#### 4.3.3 Simple Solutions Prove to Be Ineffective  
Before we describe the optimal method for integrating uncertainty information to enhance the re-identification performance, we first demonstrate that simple incorporation strategies are ineffective.  
Replacement of the Feature Vector by the Estimated Uncertainty Vector  
In light of the observed correlation in Figure 6b,d, one could hypothesize that the estimated model uncertainty may contain the same information as the feature vector. Therefore, we conducted an initial experiment to determine the extent to which re-identification results would be affected if the feature vector were replaced with the estimated model uncertainty vector. Furthermore, given that the three types of estimated uncertainty are also correlated (see Section 4.2), we also investigated the impact of replacing the feature vector with the estimated data uncertainty vector and the estimated distributional uncertainty vector.  
For given query feature vectors \(\mu^{\mathcal{Q}}\in\mathbb{R}^{Q\times d}\) and gallery feature vectors \(\mu^{\mathcal{G}}\in\mathbb{R}^{G\times d}\), the conventional computation of the distance matrix \(D^{\mu}\), which serves as the basis for calculating the rankings and subsequently the re-identification performance, is described in Equation (26).  
\[D^{\mu}=\mathfrak{d}_{cos}(\mu^{\mathcal{Q}},\mu^{\mathcal{G}}) \tag{26}\]  
This computation of the distance matrix can also be applied when the feature vector is replaced by an uncertainty vector. For given query uncertainty vector estimates \(\Sigma^{(\omega),\mathcal{Q}}\in\mathbb{R}^{Q\times d}\), \(\omega\in\{M,D,V\}\) and gallery uncertainty vector estimates \(\Sigma^{(\omega),\mathcal{G}}\in\mathbb{R}^{G\times d}\), the distance matrix \(D^{\Sigma^{(\omega)}}\) can be calculated as in Equation (27) with the variance used as the basis for the calculation. Similarly, the distance matrix \(D^{\sqrt{\Sigma^{(\omega)}}}\), which employs the standard deviation as the basis, can be calculated as in Equation (28). In the case of the standard deviation, the square root is applied element-wise to the estimated uncertainty vectors.  
\[D^{\Sigma^{(\omega)}} =\mathfrak{d}_{cos}(\Sigma^{(\omega),\mathcal{Q}},\Sigma^{(\omega ),\mathcal{G}}), \omega\in\{M,D,V\} \tag{27}\] \[D^{\sqrt{\Sigma^{(\omega)}}} =\mathfrak{d}_{cos}\Big{(}\sqrt{\Sigma^{(\omega),\mathcal{G}}}, \sqrt{\Sigma^{(\omega),\mathcal{G}}}\Big{)} \tag{28}\]  
The results for replacing the feature vectors with the estimated uncertainty vectors are reported in Table 2.  
We observe that when the standard deviation of the model uncertainty estimate was utilized to replace the feature vector (\(D^{\sqrt{\Sigma(M)}}\)), we unexpectedly obtained a relatively good result. Similarly, when the feature vector was replaced with the variance of the model uncertainty estimate (\(D^{\Sigma(M)}\)) or the standard deviation or variance of the data uncertainty estimate (\(D^{\sqrt{\Sigma(D)}},D^{\Sigma(D)}\)), the resulting outcome deviated significantly from the expected random outcome. In contrast, the distributional uncertainty estimates (\(D^{\sqrt{\Sigma(V)}},D^{\Sigma(V)}\)) are unsuitable as a replacement. Thus, we can conclude, that the model uncertainty estimate and the data uncertainty estimate contain some information that is also present in the feature vector. However, even the best result achieved with the standard deviation of the model uncertainty estimate (\(D^{\sqrt{\Sigma(M)}}\)) is significantly inferior to the results achieved with the feature vector (\(D^{\mu}\)).