sklearn marco vs micro

多类别任务的评估指标一般有的计算方式有mirco和marco之分，micro使用全体样本计算指标，marco使用各类别的指标均值。

以F1_score为例，

二分类的F1_score计算公式为：
$$F1=\frac{2\times Precision\times Recall}{Precision+Recall}$$
多分类F1_score分为：micro-f1，macro-f1

micro-f1
$$\text{ Micro }-F1=\frac{2\mathrm{P}\times R}{\mathrm{P}+\mathrm{R}}$$

$$\mathrm{P}=\frac{{\sum }_{t\in \mathcal{S}}T{P}_t}{{\sum }_{t\in S}T{P}_t+F{P}_t},\mathrm{R}=\frac{{\sum }_{t\in S}T{P}_t}{{\sum }_{t\in \mathcal{S}}T{P}_t+F{N}_t},t为类别$$

macro-f1
$$\text{ Macro }-F1=\frac{1}{\mathcal{S}}\sum _{t\in \mathcal{S}}\frac{2{\mathrm{P}}_t\times R_t}{{\mathrm{P}}_{\mathrm{t}}+{\mathrm{R}}_{\mathrm{t}}}$$

$${\mathrm{P}}_t=\frac{T{P}_t}{T{P}_t+F{P}_t},{\mathrm{R}}_t=\frac{T{P}_t}{T{P}_t+F{N}_t}$$

import numpy as np
import pandas as pd
import sklearn
from sklearn.metrics import precision_score, recall_score, f1_score
from sklearn.preprocessing import LabelBinarizer

y_true = np.array([0, 1, 2, 0, 1, 2])
y_pred = np.array([0, 2, 1, 0, 0, 1])

print("marco:")
print('precision: {}'.format(precision_score(y_true, y_pred, average='macro')))
print('recall: {}'.format(recall_score(y_true, y_pred, average='macro')))
print('f1_score: {}'.format(f1_score(y_true, y_pred, average='macro')))
print('')

print('micro')
print('precision: {}'.format(precision_score(y_true, y_pred, average='micro')))
print('recall: {}'.format(recall_score(y_true, y_pred, average='micro')))
print('f1_score: {}'.format(f1_score(y_true, y_pred, average='micro')))
print('')

print("各类别单独计算指标")
for i in range(3):
    print('label: {}'.format(i))
    y_true_new = (y_true==i).astype(int)
    y_pred_new = (y_pred==i).astype(int)
    print('precision: {}'.format(precision_score(y_true_new, y_pred_new, average='binary')))
    print('recall: {}'.format(recall_score(y_true_new, y_pred_new, average='binary')))
    print('f1_score: {}'.format(f1_score(y_true_new, y_pred_new, average='binary')))
    print(" ")

执行结果：

marco:
precision: 0.2222222222222222
recall: 0.3333333333333333
f1_score: 0.26666666666666666

micro
precision: 0.3333333333333333
recall: 0.3333333333333333
f1_score: 0.3333333333333333

各类别单独计算指标
label: 0
precision: 0.6666666666666666
recall: 1.0
f1_score: 0.8
 
label: 1
precision: 0.0
recall: 0.0
f1_score: 0.0
 
label: 2
precision: 0.0
recall: 0.0
f1_score: 0.0

验证：
$$\begin{gathered} P=\frac{2+0+0}{2+2+2}=\frac{1}{3},P=\frac{2+0+0}{3+2+1}=\frac{1}{3} \\ Micro-F1=\frac{2\mathrm{P}\times R}{\mathrm{P}+\mathrm{R}}=\frac{1}{3} \end{gathered}$$

$$Macro-F1=\frac{1}{3}(0.8+0.0+0.0)=\frac{4}{15}$$

自己的思考：找了几个资料，发现对于macro，micro的适用场景，没有详细的区分说明。我认为marco比micro更加关注类别的分布，更适合类别不平衡的情况。当然，类别不平衡时，还可以在sklearn中选用weighted参数，自己赋权，更加合适。