[机器学习]监督学习应用.梯度下降

Notation:

1.$m$ : # training examples
2.$x$ : input variables \ features
3.$y$ : output variables \”target”variables
4.$(x,y)$ : training example
5.$i_{th}$ training example : $(x^{(i)},y^{(i)})$

Flow Path

training set$\to$learning algorithm$\to$h(hypothesis)

Hyposthesis Function

New Living Area $\to$ Hypothesis $\to$ Estimate Price

Linar function(regression problems)

$h(\theta) = h_\theta(X)= \theta_0 + \theta_1X_1 + \theta_2X_2$（$X_1$ = size $X_2$ = #bedrooms $X_0 = 1$）

$\Longrightarrow$$h_\theta(X) = \sum_{k=0}^N \theta_kX_k$($\theta_i$ is called parameters)

$\Longrightarrow$$\theta_x^T$($n$ = #featrues)

$min_\theta = \frac{1}{2}\sum_{i=1}^m (h_\theta(x^{(i)}) - y^{(i)})^2 \Longrightarrow J(\theta)$

梯度下降公式推导

$\Longrightarrow$