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I know we can use SVMs probabilities after predicting validation data in order to build ROC curves. However, for CNNs, I have a binary classification problem and so the sigmoid activation function will give me probabilities of both classes. So, which probability should I use to build the ROC curve? what happens if the probabilities are close to each other?

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For binary classification problem, naturally, classes are called positives and negatives. Positive is usually a class of detection something that we are interested in, for example, spam or disease detection. According to documentation for sklearn.metrics.roc_curve, it takes as argument probabilities for positive class. For most binary classifiers, output probability usually refers to the probability of positive class (which is marked as 1 in the data). So, use probabilities of the class marked as 1 in the data.

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