Learning from noisy labels is an important concern because of the lack of accurate ground-truth labels in plenty of real-world scenarios. In practice, various approaches for this concern first make some corrections corresponding to potentially noisy-labeled instances, and then update predictive model with information of the made corrections. However, in specific areas, such as medical histopathology whole slide image analysis (MHWSIA), it is often difficult or even impossible for experts to manually achieve the noisy-free ground-truth labels which leads to labels with complex noise. This situation raises two more difficult problems: 1) the methodology of approaches making corrections corresponding to potentially noisy-labeled instances has limitations due to the complex noise existing in labels; and 2) the appropriate evaluation strategy for validation/testing is unclear because of the great difficulty in collecting the noisy-free ground-truth labels. In this paper, we focus on alleviating these two problems. For the problem 1), we present one-step abductive multi-target learning (OSAMTL) that imposes a one-step logical reasoning upon machine learning via a multi-target learning procedure to constrain the predictions of the learning model to be subject to our prior knowledge about the true target. For the problem 2), we propose a logical assessment formula (LAF) that evaluates the logical rationality of the outputs of an approach by estimating the consistencies between the predictions of the learning model and the logical facts narrated from the results of the one-step logical reasoning of OSAMTL. Applying OSAMTL and LAF to the Helicobacter pylori (H. pylori) segmentation task in MHWSIA, we show that OSAMTL is able to enable the machine learning model achieving logically more rational predictions, which is beyond various state-of-the-art approaches in handling complex noisy labels.
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