Accuracy score from confidence interval

Question

I have an algorithm which is able to make a prediction and given a confidence interval ( ex. 0.95 ) it generates the upper and lower bound for the prediction. My question is, how can i get an accuracy score ( in [0,1] ) for my prediction given the confidence interval and the output lower and upper bounds ?

My only idea was to use the bounds to compute the percentage of maximum error for the prediction, but in this way the confidence interval is not exploited in the calculation. (ex. prediction=2, upper=3, lower=1, the maximum error is (prediction-lower)/prediction or (prediction-upper)/prediction )

Answer 1

This is not really done. Anyway, a simple example off the top of my head would be:

1. Normalize relative on all the data, if that is acceptable to you

So a standard min-max scaling, get the max distance between lower and upper bounds for all the predictions, and scale each interval/distance by this max distance, this will give you a new value between 0 and 1. You have to repeat this if you get new data though, because you might get a new interval with larger distance.

2. Normalize relative to the interval

So similar to what you proposed, do $\frac{Predicted-Lower}{Upper-Lower}$ to get a value between 0 and 1, again you scale on the distance between max and min, but for each prediction individually.