计算上面程序中w和b的梯度
时间: 2024-05-21 20:11:11 浏览: 14
根据链式法则,我们需要先求出$dz$、$dw$和$db$的梯度:
$$dz = \frac{\partial L}{\partial z} = \frac{\partial L}{\partial \hat{y}} \cdot \frac{\partial \hat{y}}{\partial z} = (\hat{y} - y) \cdot w$$
$$dw = \frac{\partial L}{\partial w} = \frac{\partial L}{\partial \hat{y}} \cdot \frac{\partial \hat{y}}{\partial z} \cdot \frac{\partial z}{\partial w} = x \cdot (\hat{y} - y)$$
$$db = \frac{\partial L}{\partial b} = \frac{\partial L}{\partial \hat{y}} \cdot \frac{\partial \hat{y}}{\partial z} \cdot \frac{\partial z}{\partial b} = \hat{y} - y$$
其中,$L$为损失函数,$\hat{y}$为模型预测值,$y$为真实值,$z$为线性变换的结果,$x$为输入特征。
因此,根据以上公式可以得到:
$$dz = (\hat{y} - y) \cdot w = (0.7 - 0.8) \cdot 0.5 = -0.05$$
$$dw = x \cdot (\hat{y} - y) = 1 \cdot (0.7 - 0.8) = -0.1$$
$$db = \hat{y} - y = 0.7 - 0.8 = -0.1$$
因此,$w$和$b$的梯度分别为$-0.1$和$-0.1$。
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