# An Improved Heteroscedastic Modeling Method for Chest X-ray Image Classification with Noisy Labels
## 3 Methodology
### The Proposed GMM-HM
#### 3.2.4 Optimization
The AUC score for each pathology and the average AUC over 14 pathologies are used to evaluate the performance of the proposed method. ### Implementation Details

First, we introduce the details about how GMM is applied. In one training epoch, we fit a two-component GMM on the per-sample loss in the previous epoch to divide the training samples into a noisy and a clean set. The posterior probability of one sample whose loss belongs to the Gaussian component with a smaller mean larger than T (0.5 in the experiments) belongs to the clean set. Otherwise, it belongs to the noisy set. Second, for the noise-aware network, we perform data augmentation by randomly resizing and cropping to 224 \(\times\) 224 and randomly horizontal flipping and normalizing with the mean and standard variance of ImageNet [34] in training. During testing, the image is also resized to 224 \(\times\) 224. We train the GMM-HM with a stochastic gradient descent algorithm with an initial learning rate of 0.01. The batch size is set to 16. The threshold \(T\) in GMM is set to 0.5. On the ChestX-ray14 dataset, we train the network using stochastic gradient descent with an initial learning rate of 0.01. The learning rate is reduced by a factor of 10 after every 30 epochs. The batch size is 64. In HM and GMM-HM for both of these two datasets, we set the momentum to 0.9 and weight decay to 5e-4 in SGD, the softmax temperature to 1.5, and MC samples to 10,000. ### Comparative Studies

**Comparative Methods. ** (1) **Baseline. ** We train a ResNet-50 [1] as our baseline method. We replace the last fully connected layer with a C-dimensional fully connected layer to classify the input images, e.g., \(C=3\) on ChestX-ray2017 and \(C=14\) on ChestX-ray14. (2) **Heteroscedastic Modeling. ** We also compare our method to the original Heteroscedastic Modeling (HM) [3]. In HM, we input all the samples into the heteroscedastic layer and do not distinguish the clean or noisy samples like our proposed GMM-HM. #### 4.3.1 Results on ChestX-ray2017

Table 2 shows the results on the ChestX-ray2017 dataset. We train a strong baseline on the ChestX-ray2017 dataset with different levels of symmetric or asymmetric noise. We first analyze the symmetric noise case. When the noise level is 20%, the accuracy of the Baseline is 84.29%, the sensitivity is 84.29%, the specificity is 91.95%, and the AUC is 93.60%. By introducing the Heteroscedastic Modeling of noise labels, these four evaluation metrics are obviously improved, especially the accuracy and sensitivity (about 2%). Promoted by our GMM-HM, the performance over all the evaluation metrics is further enhanced by at least 1%. Compared with the Baseline, GMM-HM achieves a significant improvement of about 3% in accuracy and sensitivity. When the noise level increases to 40%, the entire performance of the Baseline method decreases by about 2%. We observe that the improvement with HM is slight on some metrics, e.g., specificity and AUC. On the other metrics, the performance is improved by about 1%. However, GMM-HM is not affected by the noise ratio and promotes performance improvement on all metrics by about 3%. We could obtain similar or greater improvements when the noise ratio increases to 60%. Particularly, compared with Baseline, the AUC of GMM-HM achieves a significant improvement of about 4.29%. Next, we analyze the case where the noise type is asymmetric noise. When the noise ratio is 20%, the accuracy of the Baseline is 84.94%, the sensitivity is 84.94%, the specificity is 91.96%, and the AUC is 94.46%. Similar to the symmetric noise, the performance on the four evaluation metrics is improved by introducing the Heteroscedastic Modeling for noisy samples. We could observe that the performance of most of these metrics is enhanced by over 2%, e.g., accuracy and sensitivity. The proposed GMM-HM obtains greater performance gains on all evaluation metrics, especially the sensitivity with 3.36%. When the noise ratio increases to 40%, we could observe that the performance with HM and GMM-HM is consistently improved by about 1-2%.