Neural networks

Complex hypotheses：

A supervised learning classification problem：（training set）

Using logistic regression to solve this question :

 

 

 

g refers to sigmoid function ，if it includes enough polynomial terms ，you can get a hypotheses that separates the positive and negative examples .

BUT if you have features more than two , such as house prediction , you want to predict the house will be sold in the next six months , it is a classification problem . If you use logistic regression to predict , that will be included many complicated polynomial terms . For example , if you have 100 features , then the polynomial terms will close to (n^2)/2 , that will cause over fitting problem . In this situation , if you drop some features that we can`t get a suitable separated line .

In computer vision problems , people see a car by eyes , but computer see a complex matrix or a grid of pixel intensity values . computer knows it is a car by that data set .

 a car is composed by many pixels , just in case we have the 50 * 50 pixel images , we would have 2500 pixels , learn nonlinear hypothesis by including all the features is impossible .  Because we have a total about 300M terms for the quadratic features .

In this case , if we use Neural network can get this problem done even the feature is large .