Question

Show that the gradient Descent algorithm for logistic regression: Gradient Descent $J(\theta) = -\frac{1}{m} \sum_{i=1}^{m} [y^{(i)} \log h_{\theta}(x^{(i)}) + (1 - y^{(i)}) \log (1 - h_{\theta}(x^{(i)}))]$ Want $min_{\theta} J(\theta)$: Repeat {$\theta_j := \theta_j - \alpha \frac{\partial}{\partial \theta_j} J(\theta)$ } (simultaneously update all $\theta_j$) Looks identical to linear regression: Repeat {$\theta_j := \theta_j - \alpha \sum_{i=1}^{m} (h_{\theta}(x^{(i)}) - y^{(i)})x_j^{(i)}$ } (simultaneously update all $\theta_j$)

          Show that the gradient Descent algorithm for logistic regression:
Gradient Descent
$J(\theta) = -\frac{1}{m} \sum_{i=1}^{m} [y^{(i)} \log h_{\theta}(x^{(i)}) + (1 - y^{(i)}) \log (1 - h_{\theta}(x^{(i)}))]$
Want $min_{\theta} J(\theta)$:
Repeat {$\theta_j := \theta_j - \alpha \frac{\partial}{\partial \theta_j} J(\theta)$
}
(simultaneously update all $\theta_j$)
Looks identical to linear regression:
Repeat {$\theta_j := \theta_j - \alpha \sum_{i=1}^{m} (h_{\theta}(x^{(i)}) - y^{(i)})x_j^{(i)}$
}
(simultaneously update all $\theta_j$)

Show that the gradient Descent algorithm for logistic regression:
Gradient Descent
J(θ) = -(1)/(m)∑i=1^m [y^(i)log hθ(x^(i)) + (1 - y^(i)) log (1 - hθ(x^(i)))]
Want minθ J(θ):
Repeat := - α(∂)/(∂) J(θ)

(simultaneously update all )
Looks identical to linear regression:
Repeat := - α∑i=1^m (hθ(x^(i)) - y^(i))xj^(i)

(simultaneously update all )

Added by Nicholas L.

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