I am interested in finding out how confident my model (say Logistic Regression) is in predicting the label of a new data point. For example, if it is not confident, I better abstain from making a prediction.
Logistic Regression outputs probabilities, which gives you a notion that there is confidence in prediction. But in fact, it is not. $P(y|x)$ being 0.3, doesn't tell me that the model is confident in its prediction or not. All, we can say is that it believes 100% that class A is 0.3 and other class is 0.7.
Can we use confidence intervals of LR as some sort of confidence in prediction? E.g., larger the difference between upper and lower bound for a particular data point, less confident it is, and vice-versa?
If not, how can we build confidence in our prediction? Can anybody guide me to some paper or field of study?