Logical Assessment Formula and its Principles for Evaluations without Accurate Ground-Truth Labels

Logical assessment formula (LAF) [1] was proposed to alleviate the situation where accurate ground-truth labels are not available for evaluations of an approach for a specific learning task. With a H. pylori segmentation task of medical histopathology whole slide images [1,2], evaluations based on LAF has been qualitatively shown to be able to reflect the logical rationalities of the predictions of various approaches. Comprehensive descriptions of LAF can be found in Section 2. However, the principles of LAF for evaluations without accurate ground-truth labels (AGTL) are not well revealed. In this paper, we provide comprehensive theoretical analyses to reveal the principles of LAF for evaluations without AGTL. Details of the revealed principles of LAF are presented in Section 4. From the revealed principles of LAF, we summarize, for the situation where accurate ground-truth labels are not available while multiple inaccurate targets containing various information consistent with our prior knowledge about the true target are available, the major practicability of LAF is that it can be reasonably applied for evaluations without AGTL on a more difficult task, just acting like usual strategies for evaluations with AGTL; and the minor practicability of LAF is that it can be applied for evaluations without AGTL from the logical perspective on an easier task, unable to be acting like usual strategies for evaluations with AGTL. Details of the practicability of LAF summarized from the revealed principles can be found in Section 5. To verify the practicability of LAF summarized from the revealed principles, we apply LAF on two tumour segmentation tasks in medical histopathology whole slide images (MHWSI) for breast cancer for evaluations without AGTL. Experimental results analyses of LAF applied on tumour segmentation for breast cancer support the practicability of LAF summarized from the revealed principles. Comprehensive contents can be found in Section 6 and 7.