Notation:
x(i): input variables/features
y(i): output/target variables
(x(i), y(i)): training example (pair)
training set - a list of training examples
superscripted (i) - an index into the training set (not an exponentiation)
Given a training set, we want to learn a function hθ(x) so that it is a good predictor for each value of x's corresponding y. This function is called a hypothesis function.
e.g., given a set of square feet and costs of houses, you could create a scatter plot of data
supervised learning - given the "right answer" for each example in the training set for the data
regression problem - given square feet of a living area, we want to predict a real-valued output (the price)
classification problem - given square feet of a living area, we want to predict a discrete value (if it's a house or apartment)
x: input, square feet of a living area
y: output, estimated price
hθ(x): hypothesis function that maps from x to y
Take the training set and put it through the learning algorithm.
We represent our hypothesis function with: hθ(x) = θ0 + θ1x
This is univariate (x) linear regression.
θ0 and θ1 are the parameters of the model.
We compute these parameters using the cost function.