Which of the following is most likely happening?

A classifier is trained on an imbalanced multi class dataset. After looking at the model's precision scores, you find that the micro averaging is much smaller than the macro averaging score.

The formula for precision is $$Pr = TP / (TP + FP)$$. To compute the macro-average precision of a multi-class classification, compute $$Pr$$ for each class, add them together, and then divide by the total number of classes. This can be summarized by the following formula: macro-average precision = $$(\sum_{i=1}^nPr_i) / n$$, where $$Pr_i$$ is the precision of the $$i$$th class and there are $$n$$ classes.

University of Michigan - Ann Arbor

Google

Macro-average is the average of some metric (e.g. precision or recall) among classes, where all classes are weighted equally.  Since this effectively gives a "boost" to smaller classes, macro-averages are more indicative of the precision/recall within smaller classes than within larger classes. According to the referenced article, however, macro-averaging can be bad practice when classes vary widely in their number of instances.

Macro-average

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

Micro Average vs Macro average Performance in a Multiclass classification setting

Macro-average Precision

The formula for recall is $$R = TP / (TP + FN)$$. To compute the macro-average recall of a multi-class classification, compute $$R$$ for each class, add them together, and then divide by the total number of classes. This can be summarized by the following formula: macro-average recall = $$(\sum_{i=1}^nR_i) / n$$, where $$R_i$$ is the recall of the $$i$$th class and there are $$n$$ classes.

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