PrecisionErrorEquations

From corrada.com/articles

Precision error equations

Given a collection of predictions or regressed functions from data, one can consider all possible permutations of the following equation $$\frac{1}{E} \sum_{i=1}^{E} y_i - \frac{1}{M} \sum_{j=1}^{M} y_j\,$$

Since all the estimated values can be written as \(y_{\text{estimated}} = y_{\text{true}} + \delta\,\) the above equations reduce to differences of the errors for any integers $E$ and $M$ \(\frac{1}{E} \sum_{i=1}^{E} y_i - \frac{1}{M} \sum_{j=1}^{M} y_j\,\)

The reason that these equations measure the precision and not the accuracy error is due to the invariance property of the equations themselves. One way to explain this is to ask: what happens if all predictions are shifted by some constant factor. This shift would affect all model predictions but would lead to exactly the same value for the precision error equations. We conclude from this invariance that the deltas in the difference equations really refer to the precision error.