9-3 逻辑回归算法损失函数的梯度

线性回归算法的梯度: 逻辑回归算法的梯度:

J(θ)=1m {i=1m(y^(i)y(i))i=1m(y^(i)y(i))X1(i)i=1m(y^(i)y(i))X2(i)...i=1m(y^(i)y(i))Xn(i)} =1mXbT(σ(Xbθ)y)\nabla J(\theta) = \frac{1}{m} \cdot \ \begin{Bmatrix} \sum_{i=1}^m (\hat y^{(i)}-y^{(i)}) \\ \sum_{i=1}^m (\hat y^{(i)}-y^{(i)})\cdot X_1^{(i)} \\ \sum_{i=1}^m (\hat y^{(i)}-y^{(i)})\cdot X_2^{(i)} \\ ... \\ \sum_{i=1}^m (\hat y^{(i)}-y^{(i)})\cdot X_n^{(i)} \\ \end{Bmatrix} \ = \frac{1}{m}\cdot X_b^T\cdot (\sigma(X_b\theta)-y)

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