# Probability as the Correct Term for Classifier Scores

This is more of a semantic question, but is the term probability, in the strictest sense, the correct term to use when describing the output of a predictive model that outputs values between 0 and 1? That is, if my logistic regression outputs a value 0.35 for some unseen sample, can and should that be interpreted as "there is a 35% probability of this sample being the 1 class"?

In my understanding, the definition of a probability refers to the frequency of occurrence of some event. Unless it is the case that ~35 out of every 100 samples that my classifier gives a score of 0.35 truly are of the 1 class, is it correct to call this a probability score? Would it be more accurate to just call it a prediction score if it doesn't truly reflect frequency?

• You may be interested in learning more about calibration.
– Sycorax
Commented Feb 14, 2020 at 16:12

The logistic regression in fact does produce probability output. If your process truly fits the logistic model, then you will get the probability distribution as an output too: $$Pr(y_i=1|X)=\frac{e^{X_i\beta}}{e^{X_i\beta}+1}$$