loss metric

sklearn.metrics模块

Classification metrics

accuracy_score:

\[{accuracy}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples}-1} 1(\hat{y}_i = y_i) \]

cohen_kappa_score:
\({\displaystyle \kappa \equiv {\frac {p_{o}-p_{e}}{1-p_{e}}}=1-{\frac {1-p_{o}}{1-p_{e}}},\!}\)
其中\(p_{o}\)是准确accuracy,\(p_e=\frac{(a+b)(a+c)}{(a+b+c+d)^2}+\frac{(c+d)(b+d)}{(a+b+c+d)^2}\)

confusion matrix
y_true = [2, 0, 2, 2, 0, 1]
y_pred = [0, 0, 2, 2, 0, 2]
confusion_matrix(y_true, y_pred)

classification_report
print(classification_report(y_true, y_pred))

Hamming loss

\[L_{Hamming}(y, \hat{y}) = \frac{1}{n_\text{labels}} \sum_{j=0}^{n_\text{labels} - 1} 1(\hat{y}_j \not= y_j) \]

jaccard_similarity_score
:

\[J(y_i, \hat{y}_i) = \frac{|y_i \cap \hat{y}_i|}{|y_i \cup \hat{y}_i|}(Jaccard-similarity-coefficient). \]

precision_recall_curve

\[\text{precision} = \frac{tp}{tp + fp}, \text{recall} = \frac{tp}{tp + fn}, F_\beta = (1 + \beta^2) \frac{\text{precision} \times \text{recall}}{\beta^2 \text{precision} + \text{recall}}.\]

logistic regression loss

\[L_{\log}(y, p) = -\log \operatorname{Pr}(y|p) = -(y \log (p) + (1 - y) \log (1 - p)) \]

Matthews correlation coefficient

\[MCC = \frac{tp \times tn - fp \times fn}{\sqrt{(tp + fp)(tp + fn)(tn + fp)(tn + fn)}}. \]

roc_curve

Zero one loss

\[L_{0-1}(y_i, \hat{y}_i) = 1(\hat{y}_i \not= y_i) \]

Brier score loss

\[BS = \frac{1}{N} \sum_{t=1}^{N}(f_t - o_t)^2 \]

Regression metrics

Explained variance score¶

\[{explained\_{}variance}(y, \hat{y}) = 1 - \frac{Var\{ y - \hat{y}\}}{Var\{y\}} \]

Mean absolute error

\[\text{MAE}(y, \hat{y}) = \frac{1}{n_{\text{samples}}} \sum_{i=0}^{n_{\text{samples}}-1} \left| y_i - \hat{y}_i \right|. \]

Mean squared error

\[\text{MSE}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples} - 1} (y_i - \hat{y}_i)^2. \]

Mean squared logarithmic error

\[\text{MSLE}(y, \hat{y}) = \frac{1}{n_\text{samples}} \sum_{i=0}^{n_\text{samples} - 1} (\log_e (1 + y_i) - \log_e (1 + \hat{y}_i) )^2. \]

\(R^2\)score

\[R^2(y, \hat{y}) = 1 - \frac{\sum_{i=0}^{n_{\text{samples}} - 1} (y_i - \hat{y}_i)^2}{\sum_{i=0}^{n_\text{samples} - 1} (y_i - \bar{y})^2} \]