My understanding is that a score output by a binary classifier e.g. logistic regression for an input instance, is interpreted as the probability of the instance belonging to class 1. The threshold 0.5 is used to classify the instance based on its score as follows. If the score >= 0.5, the instance belongs class1; otherwise it belongs class0.
Different thresholds can be used to classify the instance. An optimal threshold maximizes the sensitivity and specificity of the data. However, when an optimal threshold is < 0.5 e.g. 0.1, I think that it does not make sense to interpret the score as the probability of an instance belonging to class1. This is because when the score is 0.1 and the threshold 0.1 is used, the instance is classified as class1; interpreting the score as probability of belonging to class1 would contradict our common sense that the smaller the probability the less likely the event occurs; in this case, an instance is not likely (score 0.1) to belong to class1 (but it is still classified as class1 using threshold 0.1).
What would be the interpretation of the score of a binary classifier when using a threshold < 0.5?
I think for any threshold > 0.5, it makes senses that the score is interpreted as probability of belonging to class1.
Thanks David
