#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)

$$R_{lcs}=\frac {LCS(X,Y)}{m} ,m=len(X)$$ $$P_{lcs}=\frac {LCS(X,Y)}{n} ,n=len(Y)$$ $$F_{lcs}=\frac{(1+\beta^2)R_{lcs}P_{lcs}}{R_{lcs}+\beta^2P_{lcs}}$$