Supervised learning

1. Guide

    Suppose we have a dataset giving the living areas and prices of 47 houses from Portland, Oregon:

                            

    We can plot this data:

                 

   Given data like this, how can we learn to predict the prices of other houses in Portland, as a function of the size of their living areas?

 

2. Establish notation

    x⁽ⁱ⁾ denote the input features, y⁽ⁱ⁾ denote the output or target varibale that we are trying to predict.

    (x⁽ⁱ⁾, y⁽ⁱ⁾)  is called training example, and the dataset that we'll be using to learn---a list of m training example{(x⁽ⁱ⁾, y⁽ⁱ⁾); i=1...m} is called a training set.

    X denote the space of input values, and Y denote the space of output values.

    Supervised learing: giving a training set, to learn a function h: X-->Y so that h(x) is a good predictor for the corresponding value of y. For historical reasons, h is called a hypothesis. The process is therefore like this:

                                                                    

 

3. Regression problem and classification problem

    Regression problem: the target variable that we're trying to predict is continuous(such as predict price of house).

    Classification peoblem: y can take only a small number of discrete values(such as predict if a dwelling is a house or an apartment).