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.

We can compute micro-average precision by dividing the number of true positives across all classes by the sum of true positives and false positives across all classes.

More formally, let $TP_i$  and $FP_i$ be the number of true positives and false positives, respectively, in class $i$. Given a multi-class classification with $n$ classes, we can express micro-average precision as the following formula:

micro-average precision = $(\sum_{i=1}^nTP_i) / (\sum_{i=1}^n(TP_i+FP_i ))$

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Micro-average is the average of some metric (e.g. precision or recall) among classes, where classes are weighted proportionally by their number of instances. Another way of saying this is that all instances are weighted equally. Since larger classes have more instances and all instances have equal weight, micro-averages are more indicative of the precision/recall within larger classes. In other words, larger classes have more influence.

Micro-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

Micro-Average Precision

We can compute micro-average recall by dividing the number of true positives across all classes by the sum of true positives and false negatives across all classes.

More formally, let $TP_i$ and $FN_i$ be the number of true positives and false negatives, respectively, in class $i$. Given a multi-class classification with $n$ classes, we can express micro-average recall as the following formula:

micro-average recall = $(\sum_{i=1}^nTP_i) / (\sum_{i=1}^n(TP_i+FN_i ))$

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