# Few-Shot Wideband Tympanometry Classification in
## 4 Discussion
The GP was leveraged in GPGDA to characterize the manifold containing the latent variables (features) and to measure the distance between the distributions by jointly considering the first- and second-order moments (Equations (7)-(10)). In contrast, DAN exploited the MMD distance and took the first-order moment information into account only. The mean values of AUC for GPGDA at \(\lambda=0\) were smaller than those at \(\lambda=0.5\) (Table 2). The information provided by the GP on uncertainty was not exploited at \(\lambda=0\), and only the loss \(l^{c}\) generated by comparing the mean inferred from the latent variables (features) via GP with the original label was adopted to update the parameters of the feature extractors. It was equivalent to using an independent classifier (GP without uncertainty output) different from the original SoftMax classifier to update the parameters of the feature extractors in this case (\(l^{c}\) and \(l^{CE}_{r}\) as a function of Epochs followed the same steep exponential decay model; Figure 4), so from this view, GPGDA with \(\lambda=0\) could be considered to degenerate into FT. In addition, GPGDA could be regarded as using only the first-moment to measure the difference of the joint distributions if the uncertainty output by GP was not utilized. These potential reasons may explain the deterioration of AUC performance for GPGDA with \(\lambda=0\). The uncertainty loss \(l^{m}\) in GP loss \(l^{GP}\) was employed to characterize the confidence for the GP inference. It was calculated using the estimated covariance matrix, and it did not require the information on labels. The \(l^{m}\) converged significantly slower than the other two losses (\(l^{c}\) and \(l^{CE}_{r}\)), which caused \(l^{m}\) to often remain at a value greater than 0 when the other two losses were already very close to 0 (Figure 4). Therefore, on one hand, the \(l^{m}\) component in \(l^{GP}\) could prevent the algorithm from falling into the local minima during the optimization by providing guidance information from another perspective, but on the other hand, a high proportion of \(l^{m}\) in \(l^{GP}\) would make the algorithm more difficult to converge because of the slow convergence rate of \(l^{m}\). Under a practical constraint of the finite number of epochs, the difficulty of convergence also meant that the test performance may demonstrate larger fluctuations at a specific number of epochs. As a result, the standard deviation of AUC for GPGDA tended to become larger as the \(\lambda\) value increased (Table 2). The explicit calibration operation for the distributions of the network's hidden variable outputs (features) via the Gaussian processes led to good results under the constraint of limited realistic data (Table 3), and it could be considered to be play a key role in the proposed GPGDA algorithm. The underlying cause may be that the distributions of the synthetic (source) and the realistic (target) datasets were significantly different, leading to a non-negligible discrepancy between the distributions of their corresponding features obtained by the same feature extractor. Moreover, further training of the classifiers via \(l^{CE}_{r}\) was also beneficial and boosted the performance on the basis of calibrating the distributions. When the information on labels is unavailable, GP loss \(l^{GP}\) in the GPGDA algorithm can still be calculated, allowing the algorithm to employ the unlabeled realistic data. Indeed, under the same conditions, the algorithm showed better AUC performance results in the presence of unlabeled realistic data than in the absence of these data (Table 4). The weakly supervised manner of this algorithm makes it more practical in real-world WBT classification where there may be missing labels. In addition, other task-unrelated WBT data (unlabeled for the current task) can also be potentially exploited to boost the performance of the algorithm on the current task.