# An Improved Heteroscedastic Modeling Method for Chest X-ray Image Classification with Noisy Labels
## 3 Methodology
### The Proposed GMM-HM
#### 3.2.4 Optimization
Particularly, GMM-HM significantly improves the accuracy and sensitivity by 2.4%. With a larger 60% asymmetric noise, the pneumonia recognition performance largely decreases with the Baseline method. The HM introduces about 1-2% improvement on the four evaluation metrics. Particularly, HM surpasses theBaseline by about 5% on the AUC score. With GMM-HM, we observe that the pneumonia recognition performance is tremendously enhanced compared with the Baseline method, e.g., AUC with 7.63%, accuracy and sensitivity with about 5%. We empirically conclude that the data-independent pneumonia noise is properly modeled by the HM and separating the noise and clean samples could also benefit further performance enhancement. #### 4.3.2 Results on ChestX-ray14

Table 3 reports the AUC score of each pathology and the average AUC score of 14 pathologies of Baseline, HM, and GMM-HM methods on the ChestX-ray14 dataset. We train a relatively strong baseline which achieves an average AUC of 0.805. By introducing the heteroscedastic modeling for the noisy samples, the average AUC score of 14 pathologies achieves 0.812. We observe that the AUC scores of \"Emphysema\" and \"Hernia\" are obviously improved from 0.893 to 0.904 and 0.885 to 0.915, respectively. This illustrates that introducing the noise label strategy could benefit the model performance on the chestX-ray14 dataset. While further handling the noisy and clean samples separately, the proposed GMM-HM achieves the highest average AUC score of 0.822 among the three methods. Moreover, among the 14 pathologies, some of them are improved significantly, e.g., over 2% for \"Pneumonia\", \"Pneumothorax\", and \"Hernia\". The results suggest that detecting noisy samples and modeling the noisy data with a heteroscedastic layer is necessary to robustly combat noise and improve classification performance. In Table 3, we also report the performance comparisons with the state-of-the-art methods. Previous works focus on network design and performance improvement but seldom consider the noisy labels existing in ChestX-ray14. By considering the data-correlated noise, GMM-HM performs better than other methods. The average AUC score achieves 0.822, which is better than the SOTA [28]. Among the 14 pathologies, GMM-HM surpasses other methods by a large gap and has the best AUC score on the \"Hernia\" (0.945). In addition, on \"Infiltration\", \"Pneumonia\", \"Pneumothorax\", and \"Edema\", the AUC score of GMM \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**20\%**} & \multicolumn{4}{c}{**40\%**} & \multicolumn{4}{c}{**60\%**} \\ \cline{2-13}  & **Acc** & **Sens** & **Spec** & **AUC** & **Acc** & **Sens** & **Spec** & **AUC** & **Acc** & **Sens** & **Spec** & **AUC** \\ \hline \multicolumn{13}{c}{Symmetric Noise} \\ \hline Baseline & 84.29 & 84.29 & 91.95 & 93.60 & 82.69 & 90.56 & 91.69 & 78.21 & 78.21 & 88.35 & 88.45 \\ HM & 86.06 & 86.06 & 92.82 & 93.61 & 83.49 & 83.49 & 90.77 & 91.94 & 79.81 & 79.81 & 89.21 & 91.60 \\ GMM-HM & **87.34** & **87.34** & **93.28** & **95.65** & **85.26** & **85.26** & **92.81** & **94.24** & **81.57** & **81.57** & **91.73** & **92.74** \\ \hline \multicolumn{13}{c}{Asymmetric Noise} \\ \hline Baseline & 84.94 & 84.94 & 91.96 & 94.46 & 80.13 & 80.13 & 89.75 & 91.77 & 58.81 & 58.81 & 77.34 & 69.99 \\ HM & 87.02 & 87.02 & 93.43 & 94.64 & 80.29 & 80.29 & 90.90 & 92.84 & 60.42 & 78.49 & 74.47 \\ GMM-HM & **88.30** & **88.30** & **94.08** & **94.87** & **82.69** & **82.69** & **92.07** & **93.44** & **63.94** & **63.94** & **79.37** & **77.62** \\ \hline \hline \end{tabular}

* Acc: Accuracy; Sens: Sensitivity; Spec: Specificity. The best performance is shown in bold.

\end{table} 
Table 2: The experimental results on the ChestX-ray2017 dataset.