机器学习笔记
分类
准确率:所有样本中预测正确的占比
$$ accuracy =\frac {TP+TN}{TP+TN+FP+FN} = \frac {T}{T+F} $$
精确率:预测为正的样本中真正的正样本占比
$$ precision = \frac {TP}{TP+FP} = \frac {TP}{P'} $$
召回率:正样本中预测为正的占比
$$ recall = \frac{TP}{TP+FN} = \frac{TP}{P} $$
F1:精确率和召回率的调和均值
$$ \begin{align*} \frac{2}{F_1} & = \frac{1}{precision} + \frac{1}{recall}\cr F_1 & = \frac{2\cdot precision \cdot recall}{precision+recall}\cr F_1 & = \frac{2TP}{2TP + FP + FN} \cr F_1 & = \frac{2TP}{P' + P} \cr \end{align*} $$
F-score:
$$ F_{score}=(1+\beta^2)\cdot \frac{precision \cdot recall}{\beta^2\cdot precision + recall} $$
| P | N | |
|---|---|---|
| P' | TP | FP |
| N' | FN | TN |
序列
BLEU(Bilingual Evaluation understudy)
$$ CP_n(C,S)=\frac {\sum_i\sum_k\min(h_k(c_i),max_{j \in m}h_k(s_{ij}))}{\sum_i\sum_kh_k(c_j)} $$
惩罚因子BP(Brevity Penalty)
$$ b(C,S)=\begin{cases} 1, &l_c \lt l_s \cr e^{1-\frac{l_s}{l_c}}, &l_c \geq l_s \end{cases} $$
$$ BLEU_N(C,S)=b(C,S)\exp(\sum_{n=1}^N\omega_n\log CP_n(C,S)) $$
机器翻译
ROUGE(Recall-Oriented Understudy for Gisting Evaluation)
| ROUGE-N | 基于N-gram公现性统计 |
|---|---|
| ROUGE-L | 基于最长公有子句共现性精确度和召回率Fmeasure统计 |
| ROUGE-W | 代权重的最长公有子句共现性精确度和召回率Fmeasure统计 |
| ROUGE-S | 不连续二元组共现性精确度和召回率Fmeasure统计 |
ROUGE-N
$$ ROUGE-N=\frac {\sum_{S \in ReferencesSummaries}\sum_{gram_n\in S}Count_{match}(gram_n)} {\sum_{S \in ReferencesSummaries}\sum_{gram_n\in S}Count(gram_n)} $$
ROUGE-L 最长公共子句longest common subsequence(LCS)
$$ R_{lcs}=\frac {LCS(X,Y)}{m} ,m=len(X) $$
$$ P_{lcs}=\frac {LCS(X,Y)}{n} ,n=len(Y) $$
$$ F_{lcs}=\frac{(1+\beta^2)R_{lcs}P_{lcs}}{R_{lcs}+\beta^2P_{lcs}} $$