线性回归以及求解方式

Linear Regression

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Hypothesis:

Parameters:

Cost Function:

Goal:

minimize

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Gradient Descent

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Outline：

• start with some
• Keep changing to reduce ,until we end up at a minimum

Algorithm:

repeat until convergence



tips:

• (simultaneously update and )
• learning rate
  if alpha is too small, gradient descent can be slow
if alpha is too large, gradient descent can overshoot the minimum. it may fail to converge or even diverge

积分部分解释

多元线性回归

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Hypothesis:

问题有那个特征量，则预测函数为：

假设
写成矩阵形式：

故：

Cost Function:

Multiple Gradient Descent

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Algorithm:

Feature Scaling(特征缩放)

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Goal:

Get every feature into approximately a range

Aligorithm

Fearture Scaling

Mean Normalization(缩放到接近0水平)

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Goal

Replace with to make features have approximately zero mean

Algorithm

Polynomial Regression

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Advantage and Disadvantage between gradient descent and normal equation:

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Normal Equation(正规方程法)

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对代价函数求偏导

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