The True Ones: Best Guess of True Proportion of 1s

30 May

ML models are generally used to make predictions about individual observations. Sometimes, however, the business decision is based on aggregate data. For example, say a company sells pants and wants to know how many will be returned over a certain period. Say the company has an ML model that predicts the chance a customer will return a pant. A natural thing to do would be to use the individual returns to get an expected return count.

One way to get an expected return count, if the model produces calibrated probabilities, is to simply take the mean. But say that you built an ML model to predict a dichotomous variable and you only have access to categorized outputs (1s and 0s). Say for model X, for cat == 1, the OOS recall is r and precision = p. Let’s say we use the model to predict labels for another dataset. Let’s say we observe 100 1s and 200 0s. What is the best estimate of the true proportion of 1s in the new dataset?

The quantity of interest = TP + FN

TP + FN = TP/r

TP = (TP + FP)*p

TP + FN = ((TP + FP)*p)/r = 100*p/r

(TP + FN)/n = 100p/300r = p/3r

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