机器学习第二课

梯度下降算法:
Repeat
{
$\theta_j=\theta_j-\alpha\frac{\partial}{\partial\theta_j}J(\theta_0,\theta_1...\theta_n)$θj​=θj​−α∂θj​∂​J(θ0​,θ1​...θn​)
}simultaneously update for every j=0,1…n)

$\theta_j=\theta_j-\alpha\frac{1}{m}\sum_{i=1}^{m} (h_{\theta}(x^{(i)})-y^{(i)})x_j^{(i)}$θj​=θj​−αm1​i=1∑m​(hθ​(x(i))−y(i))xj(i)​
Feature Scaling以及Mean normalizaition

$\alpha$α太大：slow convergence
$\alpha$α太小：J($\theta$θ) mat not decrease on every iteration,may not converge
尝试不同的$\alpha$α，绘制J($\theta$θ)随迭代次数变化的曲线

polynominal regression(多项式回归)

Normal equation(正规方程)

$\frac{\partial}{\partial\theta_j}J(\theta)=0$∂θj​∂​J(θ)=0 for every j

Gradient Descent 和 Normal Equation各自的优缺点