常用函式

softmax

$$softmax(x)_i = \frac {e^{x_i}}{\sum _j e^{x_j}}$$

sigmoid

$$\sigma(x) = \frac{1}{1+e^{-x}}$$

gradient of sigmoid

$$σ′(x) = σ(x)(1 − σ(x))$$

tanh

$$\tanh(x) = \frac{1-e^{-2x}}{1+e^{-2x}}$$

ReLU

$$ReLU(x) = max(0,x)$$

cross-entropy cost

$$CE(y,\hat y) = − \sum_i y_ilog(\hat y_i)$$

評測指標

準確率

$$Precision(\%) = \frac{True positive}{(True positive+False positive)} \times 100 \%$$

召回率

$$Recall(\%) = \frac{True positive}{(True negative+False negative)} \times 100 \%$$

F1-score

$$F1-Score = \frac{2}{\frac{1}{p}+\frac{1}{r}}$$
或者
$$F1-Score = \frac{2 \times P \times R}{P+R} = \frac {2 \times TP}{樣本總數 + TP - TN}$$

MSE: Mean Squared Error

$$MSE = \frac{1}{m} \sum_{i=1}^{m}{({\hat y^{(i)} - y^{(i)}})}^2$$

RMSE

$$RMSE =\sqrt{ \frac{1}{m} \sum_{i=1}^{m}{({\hat y^{(i)} - y^{(i)}})}^2 }$$

MAE :Mean Absolute Error

$$MAE = \frac{1}{m} \sum_{i=1}^{m}{| \hat y^{(i)} - y^{(i)} |}$$

• 均方誤差是指引數估計值與引數真值之差平方的期望值，可以評價資料的變化程度，MSE的值越小，說明預測模型描述實驗資料具有更好的精確度.
• 均方根誤差是均方誤差的算術平方根
• 平均絕對誤差是絕對誤差的平均值，能更好地反映預測值誤差的實際情況.