micro average is the same for precision, recall, f1_score, fbeta_score

[srikris]

For the multi-class case, the micro average option seems to result in mathematically equivalent definitions for precision_score and recall_score (and as a result equivalent f1_score, and fbeta_score, and accuracy_score).

Am I missing something? Here is my argument:

For the multi-class setting, let p_m and r_m denote the micro precision. If we define

p_m = tp / (tp + fp)
r_m = tp / (tp + fn)

where tp, fp, tn, fn are the total number of global true positives, false positives, true negatives, and false negatives (this seems to be my understanding of how this is implemented), then by definition fp = tn because in for an incorrect prediction (A, B) if you are a false positive with respect to class A, then you are a true negative with respect to class B so summing over them result in all the incorrect predictions. Hence, they are the same as accuracy

Here is the code that got me thinking about this.

from sklearn.metrics import *
import random

y_pred = [random.randint(0, 2) for i in range(100)]
y_true = [random.randint(0, 2) for i in range(100)]

print precision_score(y_true, y_pred, average='micro')
print recall_score(y_true, y_pred, average='micro')
print f1_score(y_true, y_pred, average='micro')
print accuracy_score(y_true, y_pred)

0.34000000000000002
0.34000000000000002
0.34000000000000002
0.34000000000000002

[jnothman]

As is written in the documentation: "Note that for “micro”-averaging in a
multiclass setting will produce equal precision, recall and [image: F],
while “weighted” averaging may produce an F-score that is not between
precision and recall."
http://scikit-learn.org/stable/modules/model_evaluation.html

But if you drop a majority label, using the labels parameter, then
micro-averaging differs from accuracy, and precision differs from recall.

On 4 November 2015 at 19:14, Srikrishna Sridhar notifications@github.com
wrote:

The micro average option seems to result in mathematically equivalent
definitions for precision_score and recall_score (and as a result
equivalent to the f1_score, and fbeta_score).

Am I missing something? Here is my argument:

For the multi-class setting, let p_m and r_m denote the micro precision.
If we define

p_m = tp / (tp + fp)
r_m = tp / (tp + fn)

where tp, fp, tn, fn are the total number of true positives, false
positives, true negatives, and false negatives (this seems to be my
understanding of how this is implemented), then by definition fp = tn
because if you are a false positive with respect to class A, then you are
a true negative with respect to class B.

Based on the definition here , we have

p_m = stp / (stp + sfp)
r_m = stp / (stp + sfn)

where sfp

Here is the code that got me thinking about this.

from sklearn.metrics import *
import random

y_pred = [random.randint(0, 2) for i in range(100)]
y_true = [random.randint(0, 2) for i in range(100)]

print precision_score(y_true, y_pred, average='micro')
print recall_score(y_true, y_pred, average='micro')
print f1_score(y_true, y_pred, average='micro')

0.34000000000000002
0.34000000000000002
0.34000000000000002

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