## 5 Discussion  
This article proposed a deep-learning-based hierarchical approach for estimating the biological age of a person wearing a face mask in a group-specific manner. In the hierarchical approach, the error spaces were squeezed by introducing the group classification approach prior to the age regression stage of the computation. Firstly, we classified the sample of 101 age classes into three major age groups named child, adult, and elder. Next, the specific network designed for each age group carried out the age estimation process through regression-via-classification strategies described in Section 3.  
In the system design, we addressed two crucial types of deep learning model uncertainty: epistemic uncertainty and aleatoric uncertainty. Epistemic uncertainty occurred due to data inadequacy and systematic bias while collecting samples observed partially because some age classes (i.e., 1, 3, 4, or 97) contained very few image samples (<100) for training. Similarly, there was some randomness in the input data due to pixel noise, and the incorrect annotation caused aleatoric uncertainty. We tried to mitigate both the model uncertainties by data augmentation, data supplementation, and manually filtering out the noisy data as much as possible.  
The proposed hierarchical approach demonstrates comprehensive results over the synthetic IMDB-WIKI masked face image dataset in anticipation of real age estimation. From the experimental results presented in Figure 7, it is quite evident that the hierarchical approach is marginally better than the singular approach, apart from with regard to deep learning model selection. If we consider the cumulative score graph presented in Figure 10, as the error threshold value is less, the difference between the approaches is quite evident. Furthermore, the performance of the models while experimenting on individual age group  
Figure 11: Wilcoxon Signed-Rank statistical significance test analysis over the deployed models between the proposed hierarchical approach and conventional approach for masked face age estimation. In every test, models give a \(p\)-value of less than 0.05 which statistically proves that the model’s performances are significantly different. The \(p\)-values are presented in the form of \(-log_{10}(p-\text{value})\) for clear perception.  
is presented quantitively and graphically in Section 4. Our models demonstrated enviable performances in the case of the child and adult group, whereas they were still deficient when handling adult faces, since the changes in features among adults are relatively stable and indifferent.  
It is worth mentioning that lightweight models demonstrate a slightly higher MAE than deeper models but are competent enough for deployment in low-end devices. Additionally, we performed a statistical significance test to ensure the system's robustness and proved that the performance achieved through hierarchical and singular approaches was significantly different (see Section 4 and Figure 11).  
In future research, we will try to build a new face mask dataset by maintaining parity among the age classes since the amount of data in every age is insufficient to train a deep learning model for a complex problem such as real age estimation. We will try to lessen the mean absolute error in the adult group, which was somewhat higher than the other groups formulated in this experiment.