Hands on deep learning -- Introduction to linear regression model

About house price forecast

1、 A simplified model

hypothesis 1： The key factor affecting the house price is the number of bedrooms , Number of toilets and living area , Write it down as x1,x2,x3.

hypothesis 2： Weighted sum of the key factors of the transaction

                 y=w1x1+w2x2+w3x3+bquanzhong

The actual values of weights and deviations are determined later

2、 Linear model

• Given n Dimension input ：

• The linear model has a n Weight and a scalar deviation ：

• The output is the weighted sum of the inputs ：

Vector version ：y=<w,x+b 

 3、 The linear model can be regarded as a single-layer neural network

  

 4、 Neural network comes from neuroscience

5、 Measure estimated quality

Compare the actual value with the estimated value , For example, the price and valuation of the house

hypothesis y Is the real value ,y^ It's an estimate , We can compare ：

This is called the square loss . 

6、 Training data

Collect some data points to determine parameter values （ Weight and bias ）, For example, in the past 6 A house sold for months , This is called training data .

Usually the more data the better .

Suppose we youn Samples , remember ：

7、 Parameter learning

Loss of training ：（ Loss function ）

Minimize losses to learn parameters ：

 8、 Display solution

Add the deviation to the weight

 

  Loss is a convex function , So the optimal solution satisfies ：

9、 summary ：

• Linear regression is right n Weighting of dimension input , Plus bias
• Use the square loss to measure the difference between the predicted value and the real value
• Linear regression has an explicit solution
• Linear regression can be regarded as a single-layer neural network