In the previous article in this series, we showed that common ensemble models like random forest and gradient boosting are uncalibrated: they are not guaranteed to estimate aggregates or rollups of the data in an unbiased way. However, they can be preferable to calibrated models such as linear or generalized linear regression, when they make more accurate predictions on individuals. In this article, we’ll demonstrate one ad-hoc method for calibrating an uncalibrated model with respect to specific grouping variables. This "polishing step" potentially returns a model that estimates certain rollups in an unbiased way, while retaining good performance on individual predictions.
Continuing our series of reading out loud from a single page of a statistics book we look at page 224 of the 1972 Dover edition of Leonard J. Savage’s “The Foundations of Statistics.” On this page we are treated to an example attributed to Leo A. Goodman in 1953 that illustrates how for normally distributed data the maximum likelihood, unbiased, and minimum variance estimators of variance are in fact typically three different values. So in the spirit of gamesmanship you always have at least two reasons to call anybody else’s estimator incorrect. Continue reading Bias/variance tradeoff as gamesmanship