Machine Learning Andrew Ng -4. Linear Regression with multiple variables

4.1 Multiple features (多特征量)

Multiple features (variables)

Size $(x_1)$(x1​)	Number of bedrooms$(x_2)$(x2​)	Number of floors$(x_3)$(x3​)	Age of homes$(x_4)$(x4​)	Price$(y)$(y)
2104	5	1	45	460
1416	3	2	40	232
1534	3	2	30	315
852	2	1	36	178
…	…	…	…	…

Notation :

• $n$n = number of features
• $x^{(i)}$x(i)= input (features) of $i^{th}$ith training example
• $x_j^{(i)}$xj(i)​ = value of feature $j$j in $i^{th}$ith training example

Hypothesis :

previously : $h_{\theta}(x) = \theta_0 + \theta_1x$hθ​(x)=θ0​+θ1​x

now : $h_{\theta}(x) = \theta_0+\theta_1x_1+\theta_2x_2+\theta_3x_3+\theta_4x_4$hθ​(x)=θ0​+θ1​x1​+θ2​x2​+θ3​x3​+θ4​x4​

Multivariate linear regression 多元线性回归

4.2 Gradient descent for multiple variables

How to fit the parameters of that hypothesis ? How to use gradient descent for linear regression with multiple features ?

4.3 Gradient descent in practice I : Feature Scaling(特征缩放)

Feature Scaling : Get every feature into approximately a $-1 \leqslant x_i\leqslant 1$−1⩽xi​⩽1 range.

Mean normalization (均值归一化) ：

4.4 Gradient descent in practice II : Learning rate

4.5 Features and polynomial regression (特征和多项式回归)

Choosing feature

The price could be a quadratic function (二次函数), or a cubic function (三次函数)

now feature scaling is more important

How to choose features ? Discuss later…

4.6 Normal equation (正规方程)

Normal equation : Method to solve for $\theta$θ analytically.

One step, you get to the optimal value right there.

这里X矩阵上下标大概率写错了

Feature Scaling is no need

When choose gradient descent when choose normal equation ?

4.7 Normal equation and non-invertibility