# An Improved Heteroscedastic Modeling Method for Chest X-ray Image Classification with Noisy Labels
## 3 Methodology
### The Proposed GMM-HM
#### 3.2.4 Optimization
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline
**Methods** & **Atel** & **Card** & **Effu** & **Infi** & **Mass** & **Nodule** & **Pnel** & **Pne2** & **Cons** & **Edem** & **Emph** & **Fibr** & **PT** & **Hern** & **Mean** \\ \hline
[4] & 0.700 & 0.810 & 0.759 & 0.661 & 0.693 & 0.669 & 0.658 & 0.799 & 0.703 & 0.805 & 0.833 & 0.786 & 0.684 & 0.872 & 0.745 \\
[5] & 0.766 & 0.801 & 0.797 & **0.751** & 0.760 & 0.741 & **0.778** & 0.800 & **0.787** & 0.820 & 0.773 & 0.765 & 0.759 & 0.748 & 0.775 \\
[12] & 0.756 & 0.887 & 0.819 & 0.689 & 0.814 & 0.755 & 0.729 & 0.850 & 0.728 & 0.848 & 0.908 & 0.818 & 0.765 & 0.875 & 0.803 \\
[35] & 0.767 & 0.883 & 0.828 & 0.709 & 0.821 & 0.758 & 0.731 & 0.846 & 0.745 & 0.835 & 0.895 & 0.818 & 0.761 & 0.896 & 0.807 \\
[14] & 0.779 & 0.879 & 0.824 & 0.694 & 0.831 & 0.766 & 0.726 & 0.858 & 0.758 & 0.850 & 0.909 & 0.832 & 0.778 & 0.906 & 0.814 \\
[28] & **0.785** & **0.892** & **0.836** & 0.710 & 0.826 & 0.755 & 0.735 & 0.847 & 0.747 & 0.837 & **0.925** & **0.838** & 0.785 & 0.905 & 0.816 \\ \hline Baseline & 0.774 & 0.883 & 0.825 & 0.700 & 0.818 & 0.759 & 0.710 & 0.842 & 0.746 & 0.843 & 0.893 & 0.822 & 0.770 & 0.885 & 0.805 \\ HM & 0.777 & 0.887 & 0.830 & 0.702 & 0.827 & 0.770 & 0.717 & 0.855 & 0.747 & 0.845 & 0.904 & 0.819 & 0.777 & 0.915 & 0.812 \\ GMM-HM & 0.764 & 0.887 & 0.824 & 0.720 & **0.836** & **0.774** & **0.743** & **0.887** & 0.759 & **0.857** & 0.901 & 0.825 & 0.790 & **0.945** & **0.822** \\ \hline \hline \end{tabular}

* The 14 pathologies are Atelectasis, Cardiomegaly, Effusion, Infiltration, Mass, Nodule, Pneumonia, Pneumothorax, Consolidation, Edema, Emphysema, Fibrosis, Pleural Thickening, and Hernia, respectively. For each column, the best results are highlighted in bold.

\end{table} 
Table 3: Comparisons of GMM-HM with Baseline and HM methods on ChestX-ray14. HM also achieves a new state of the art. Basically, the proposed GMM-HM achieves comparable or even better performance compared with the state-of-the-art methods. #### 4.3.3 Feature Visualization

Figure 3 visualizes the features of the Baseline, HM, and GMM-HM methods with t-SNE [36] on different datasets. On the ChestX-ray2017 dataset, with the Baseline method, shown in Figure 1d, pneumonia and normal samples locate very close, which makes them difficult to distinguish. With HM, the distances between pneumonia and normal samples become larger, but the bacterial and viral pneumonia samples are still difficult to correctly classify (Figure 1e). With GMM-HM, we observe that the features of normal and pneumonia, even the bacterial and viral pneumonia samples, are further separated, which leads to easy classification (Figure 1f). As shown in Tables 2 and 3, GMM-HM also exceeds the HM and Baseline methods by a large gap and benefits from better feature representation. On the ChestX-ray14 dataset, as shown in Figure 3, we randomly select two pathologies to show the feature distributions and could also conclude that the proposed GMM-HM is superior to the HM and the Baseline methods. ## 5 Conclusions

In this paper, we rethink heteroscedastic modeling for chest X-ray image classification with noisy labels. Rather than inputting all the samples into the heteroscedastic layer, we propose a novel framework that considers the clean and noisy samples separately. A GMM-based noise detector and an HM-based noise-aware classification are integrated into a framework to robustly detect noisy samples and correctly classify the input images. Experimental results demonstrate the superiority of the proposed framework for pneumonia classification and multi-label disease classification tasks. In the future, instead of imposing a classification step between clean and noisy, we would consider keeping the conditional probabilities of the GMM and integrating them into the classification decision under a Bayesian approach framework. Q.G. and Q.C. (Formal analysis, Validation, Writing-Review, Editing, Experiments, Draft writing), Y.H. (Supervision, Writing-Review).