# Improving Re-Identification by Estimating and Utilizing Diverse Uncertainty Types for Embeddings
## 2 Related Work
### Uncertainty Quantification for Feature Vectors
#### 2.1.1 Quantification of Data Uncertainty  
To estimate uncertainties for feature vectors, in related work, most often probabilistic embeddings [21] are used, which are sometimes also referred to as stochastic embeddings [29]. Probabilistic Embeddings for Data Uncertainty Estimation  
Probabilistic embeddings were first introduced for natural language processing [20; 30] and later, based on the example of face recognition [21; 31], also for computer vision tasks. The key idea of probabilistic embeddings is to estimate a mean and a variance vector instead of a point estimate for the feature vector. The variance vector is interpreted as a diagonal covariance matrix. Therefore, each output is represented as a multivariate normal distribution in the embedding space. The mean vector represents the feature vector and the variance vector represents the data uncertainty of the feature vector elements. Probabilistic embeddings have been widely used for computer vision tasks, e.g., for face recognition [21; 31; 32; 33], few-shot recognition [29], emotion recognition [34], human pose embeddings [35], image retrieval [36; 37; 38], 3D shape retrieval [39], point cloud instance segmentation [40], self-supervised and representation learning [41; 42; 43; 44; 45], multi-source domain adaptation [47], vision-language embedding alignment [48; 49; 50], and person re-identification [51; 52; 53; 54; 25]. In the majority of these approaches, a Gaussian distribution has been used to model the uncertainty. Only few approaches [28; 33] present methods for deviating from a Gaussian distribution. To get a definite-valued output for further processing, most of these works sample from this distribution, which is also the way variational autoencoders (VAEs) [55] handle the distribution in the latent space. Some approaches [56; 21; 52] use the distributions directly. [PERSON] et al. [25] use the variance information to weight the mean vector. The estimated uncertainty in probabilistic embeddings represents only data uncertainty. Therefore, these probabilistic embeddings cannot quantify model uncertainty or distributional uncertainty by themselves. To date, only one alternative to probabilistic embeddings has been proposed for the estimation of data uncertainty. [PERSON] et al. [23] propose a method for estimating a kind of data uncertainty, which they then use to compute uncertainty-based weighting factors in the triplet loss. However, the uncertainty they estimate does not correspond to the mathematical model of data uncertainty. Therefore, probabilistic embeddings represent the only mathematically grounded approach for estimating data uncertainty for feature vectors that has been proposed in the state of the art. Quantification of Model Uncertainty  
Quantifying model uncertainty for feature vectors is addressed rarely. Approaches have only been proposed for image captioning [24] and person re-identification [22; 23; 25]. Bayesian Neural Networks for Model Uncertainty Estimation  
All these approaches [22; 23; 24; 25] use Bayesian Neural Networks (BNNs) to estimate the model uncertainty. BNNs replace scalar weights with a distribution over them and then use approaches such as Markov Chain Monte Carlo or Variational Inference to update the distribution such that a good set of weights becomes more and more likely. They are not very popular in deep neural networks, since they suffer from performance problems and are hard to train. As a compromise to approximate model uncertainty with limited extra computation, applying a Bayesian component on top of a deterministic backbone is a popular choice. Indeed, the re-identification approaches [22; 23; 25] all use a Bayesian module on top of a deterministic backbone. In this Bayesian module, Monte Carlo Dropout is used to sample \(K\) models to estimate the model uncertainty. Joint Estimation of Data and Model Uncertainty  
Only few approaches [23; 25] attempt to jointly estimate both data uncertainty and model uncertainty for feature vectors.