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Is there any way of selecting the best possible threshold to minimize the number of false positives and false negatives (to get the best possible minimized combination of false +ves and -ves)?

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The optimal threshold will ideally minimize the combined loss function you obtain by selecting a false positive or a false negative. If both are considered equally undesirable, you can generate a receiver-operating characteristic (ROC) curve and then determine the point which is closest in linear distance to the 100% sensitivity and specificity point.

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