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This is a cross-posting from a different perspective of a question asked here: Converting weighted value to probability .

For a disease classification problem, I trained a deep learning model to predict the probability score of a disease based on images only. During the training time, I only had access to labeled images without any other patient-related data. The model gives a probability score (in the range 0 to 1) based on an input image. Now, I would like to make the prediction more robust by incorporating expert knowledge as a subjective probability. For that reason, we have created a set of questionnaires that will be asked to the patient to assist the image-based analysis. We have collected opinions from human experts (16 doctors) and they already assigned weights to the answers (in the range [-1,3], where, -1 means low probability of the disease, 3 means high probability). A sample (say from 3 doctors) is shown in the following table:

enter image description here

Now, during actual classification I can get a weighted value based on the answer of the user using following equation:

$$\scriptsize Value = {{{Symptom_1} * {(AvgWeight_1)} + {Symptom_2} * {(AvgWeight_2)} + {Symptom_3} * {(AvgWeight_3)}} \over {3}}$$

where, Symptom can be either 0 or 1 (present or absent). The result will be in the range [-1,3], but I want to convert it to a probability score in the range [0,1]. It is not sufficient to convert the obtained value to [0,1] range using:

OldRange = (OldMax - OldMin)  
NewRange = (NewMax - NewMin)  
NewValue = (((OldValue - OldMin) * NewRange) / OldRange) + NewMin 

I want two probabilities: one from the image-based deep learning model, another from subjective expert knowledge based on questionnaires, and make the final prediction based on these two probabilities. Is it okay to ask the doctors to define the probability range for their score (like -1 to 0: maybe 0.25 probability and so on and then translate the obtained value in this range? Thanks in advance for your feedback.

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