In the following section, we either describe proof of for implication or equivalences of certain conditionsstudiedinthiswork. We use a different formulation of the relative-bias conditionduetoProposition5. C = BM, andC = BX X, hence we can define L=BX. Lemma 2. The assumption in Definition 4 implies the assumption in Definition 1 withν = J k Likewise, qG = W1/2CV 1/20 X (XV 10 X) 1ϵG is distributed asN(0,Ik). The last final inequality in the statement of the probability follows from taking a square root and triangleinequality,whichfinishestheproof.

The 'macro F1' metric is frequently used to evaluate binary, multi-class and multi-label classification problems. Yet, we find that there exist two different formulas to calculate this quantity. In this note, we show that only under rare circumstances, the two computations can be considered equivalent. More specifically, one formula well 'rewards' classifiers which produce a skewed error type distribution. In fact, the difference in outcome of the two computations can be as high as 0.5. Finally, we show that the two computations may not only diverge in their scalar result but also lead to different classifier rankings.