## 4 Discussion
### Case-Level Nodal Status Prediction: A Classic Needle-in-Haystack Challenge  
In the presented work, we face a typical needle-in-haystack problem with large images from which only small parts potentially contain predictive features. We can demonstrate that approximately 10% of the tiles bear significance in this context (compare Section 3.3 and Figure 2). The data set can be considered very noisy with such a low frequency of informative tiles or correct labels. Coupled with the minimal contrast between informative and non-informative feature vectors in the latent space, as assessed by close-to-zero silhouette scores (see Figure 2(B1,B2)), this complicates the training of machine learning models significantly [49]. Against this challenging background, we compared two method  
Figure 4: **Confusion matrix for MIL model with exemplary tiles. ** The validation set (defined as 0.25 of the entire data set) comprises 31 cases or rather bags with 27 nodal negative cases (N\(-\)) and 14 nodal positive cases (N+). A total of 18 cases are correctly predicted by the MIL model as N\(-\); and 14 cases are predicted as N+. 9 cases are false positive and 0 cases are false-negative. In summary, for the validation data set an accuracy of 0.756 and an F1-score of 0.737 is achieved. Based on the pseudo-probabilities of the network an AUC of 0.870 can be achieved. From each evaluated case, the 10 most informative tiles or the tiles with the highest significance for the respective decision are selected. AUC: area under the receiver operator characteristics curve. ologically different approaches addressing such a task: an image- and a tile-based one. First, in the tile-based approach, we convert the problem into a noisy label problem by working on the tile level. This has the advantage that such noisy label problems are well known in the literature and that there are several approaches to mitigate it [44; 45; 49]. Evaluating the numerous methods proposed in the literature for handling noisy label scenarios would have exceeded the scope of this paper [49]. In short, the data, the loss function, the model and/or the training settings can be adjusted to work on noisily labeled data sets [49]. From the approaches around the training settings, there are, for example, co-teaching approaches where two models are trained in parallel, updating each other [45]. For our data set, for instance, approaches based on analysis and further pre-processing are not promising, as shown in the latent space representation. In our data, as shown in Figure 2 and measured by the silhouette score, there are no distinct, pre-formed clusters to separate for in the latent space. In regard to published approaches to train a model with a noisily labeled data set, we can show that independently of countermeasures like early stopping, as the probably most easy noisy label technique, the models memorize the cases based on their staining (compare Section 3.1). Amongst the data-based approaches is the extensive usage of image augmentation techniques that modify the images before feeding into the model. One major advantage of the tile-based approach is that these standard techniques can be used without implementation effort. In regard to data augmentation techniques, however, we can demonstrate that widely recognized memorization effects in such a setting cannot be mitigated despite extensive usage of data augmentation methods, even when incorporating color normalization (compare Section 3.1 with Table 2). Second, in the case-based approach, we convert the needle-in-haystack task to a multi-instance learning setting. Approaches in this context are designed to find the informative instances (the needles in the given analogy) within a given bag of mostly non-informative instances (the hay fibers or the haystack) [32; 34; 50]. Our contribution to this approach is adapting data augmentation techniques. Of note, the above-mentioned standard techniques applied on the image level prior to the model do not work.