CourseMachine learning：Week 2-Lecture1-Gradient Descent For Multiple Variables
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Gradient Descent For Multiple Variables
问题提出：Week2的梯度下降问题由单一变量转变成了多变量：
相应的公式如下：
梯度下降算法
[
egin{array}{l}{ ext { repeat until convergence: }{} { heta_{j}:= heta_{j}-alpha frac{1}{m} sum_{i=1}^{m}left(h hetaleft(x^{(i)}
ight)-y^{(i)}
ight) cdot x_{j}^{(i)} quad ext { for } j:=0 ldots n} {}}end{array}
]
也就是：
[
egin{array}{l}{ ext { repeat until convergence: }{} { heta_{0}:= heta_{0}-alpha frac{1}{m} sum_{i=1}^{m}left(h_{ heta}left(x^{(i)}
ight)-y^{(i)}
ight) cdot x_{0}^{(i)}} { heta_{1}:= heta_{1}-alpha frac{1}{m} sum_{i=1}^{m}left(h_{ heta}left(x^{(i)}
ight)-y^{(i)}
ight) cdot x_{1}^{(i)}} { heta_{2}:= heta_{2}-alpha frac{1}{m} sum_{i=1}^{m}left(h_{ heta}left(x^{(i)}
ight)-y^{(i)}
ight) cdot x_{2}^{(i)}} {cdots} {}^{cdots}}end{array}
]
( heta_{0})、( heta_{1})、( heta_{2})...这些参数要同时更新
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