Micro- and macro-averages

https://datascience.stackexchange.com/questions/15989/micro-average-vs-macro-average-performance-in-a-multiclass-classification-settin/16001

Micro- and macro-averages (for whatever metric) will compute slightly different things, and thus their interpretation differs.

 

A macro-average will compute the metric independently for each class and then take the average (hence treating all classes equally), whereas a micro-average will aggregate the contributions of all classes to compute the average metric. In a multi-class classification setup, micro-average is preferable if you suspect there might be class imbalance (i.e you may have many more examples of one class than of other classes).

To illustrate why, take for example precision Pr=TP(TP+FP)Pr=TP(TP+FP). Let's imagine you have a One-vs-All(there is only one correct class output per example) multi-class classification system with four classes and the following numbers when tested:

• Class A: 1 TP and 1 FP
• Class B: 10 TP and 90 FP
• Class C: 1 TP and 1 FP
• Class D: 1 TP and 1 FP

You can see easily that PrA=PrC=PrD=0.5PrA=PrC=PrD=0.5, whereas PrB=0.1PrB=0.1.

• A macro-average will then compute: Pr=0.5+0.1+0.5+0.54=0.4Pr=0.5+0.1+0.5+0.54=0.4
• A micro-average will compute: Pr=1+10+1+12+100+2+2=0.123Pr=1+10+1+12+100+2+2=0.123

These are quite different values for precision. Intuitively, in the macro-average the "good" precision (0.5) of classes A, C and D is contributing to maintain a "decent" overall precision (0.4). While this is technically true (across classes, the average precision is 0.4), it is a bit misleading, since a large number of examples are not properly classified. These examples predominantly correspond to class B, so they only contribute 1/4 towards the average in spite of constituting 94.3% of your test data. The micro-average will adequately capture this class imbalance, and bring the overall precision average down to 0.123 (more in line with the precision of the dominating class B (0.1)).