# An Improved Heteroscedastic Modeling Method for Chest X-ray Image Classification with Noisy Labels
## 1 Introduction  
The chest X-ray is one of the most common examination methods to diagnose thorax diseases in medical screening. In practice, the diagnosis system needs a large amount of accurately labeled data to train a deep model. Manually distinguishing different pathologies in screening is a time-consuming and labor-intensive task. Moreover, a large number of noisy labels are also easily introduced in the annotations of chest X-ray images. First, chest X-rays caused by different causative agents usually present similarities in appearance, which make it difficult to distinguish. Furthermore, the noisy labels could also originate from other kinds of factors, e.g., inter-observer variability, annotation errors, or errors generated by the annotation algorithms. Therefore, it is important to explore a robust, accurate, computer-aided diagnosis system with noisy labels to assist in diagnosing radiographs. [PERSON] et al. [3] propose heteroscedastic modeling (HM) that places a multivariate normally distributed latent variable on the final hidden layer of a neural network classifier for the heteroscedastic label noise. HM breaks the homoscedasticity assumptions in network optimization with a cross-entropy loss function. However, for most of the existing datasets, only parts of the samples are wrongly annotated. Modeling all the samples with the relaxed hypothesis, especially the large number of clean samples, would affect the network convergence and increase the burden of network optimization. In Figure 1e, we could observe that the distance between the normal and the pneumonia is expanded with HM. However, the bacterial and viral pneumonia samples still locate very close and are difficult to recognize. Therefore, to enhance efficiency, it is necessary to handle the clean and noisy samples individually. In this paper, rather than model all the samples in one fell swoop as in [3], we propose to consider the clean and noisy samples separately and construct a novel framework that integrates noise detection and noise-aware classification for chest X-ray image classification with noisy labels. The noise detection module builds on a Gaussian Mixture Model (GMM) to judge whether one sample is clean or noisy. The noise-aware classification network consists of two branches that extract the specific features for clean and noisy samples and classify the input images. For the clean samples, we input them into the backbone network and classify them as usual, while for the noisy samples, we add a heteroscedastic layer to model the aleatoric uncertainty due to the data-dependent label noise. As shown in Figure 1f, by introducing noise detection and HM, the feature distribution of different kinds of samples is much easier to distinguish compared with that of HM. We verify the effectiveness of the proposed method by conducting extensive experiments on a pediatric pneumonia dataset (very easily introducing noise), ChestX-ray2017, and a real noisy dataset, ChestX-ray14. Empirically, GMM-HM is superior to HM in recognition performance. We summarize the contributions of this work as follows:  
* We revisit Heteroscedastic Modeling and illustrate that it is superior for modeling the clean and noisy samples separately, rather than modeling all images in one fell swoop for chest X-ray image classification with noisy labels. Figure 1: Examples of (**a**) Normal, (**b**) Bacterial Pneumonia, (**c**) Viral Pneumonia, and (**d–f**) are the visualized t-SNE feature distributions of the Baseline, HM, and the proposed GMM-HM methods (with 20% asymmetric noise on the ChestX-ray2017 dataset [2]). * We propose a novel GMM-HM that integrates a GMM-based noise detector and an HM-based noise-aware classification into a unified framework to classify the chest X-ray images with noisy labels. * We present a superior performance improvement on both the ChestX-ray2017 and the ChestX-ray14 datasets. The proposed GMM-HM shows strongly superior performance compared with the baseline and HM methods on symmetric and asymmetric noise on the ChestX-ray2017 dataset.