CS229 Lect. 2

Linear Regression

Linear regression is one of the simplest learning algorithms. This is a supervised learning algorithm because the data is labeled.

Ex: Predict the price of garden hoses

Training -> learning algo -> hypothesis func. $h$

The hypothesis is $h:X\to Y$ where $h(x\in X)={\theta }_0+{\theta }_{1}x$ (affine function). This assumes that we have one variable $x$.

If we have two variables (note that complex phenomena generally require many variables to be accurately predicted, e.g. thousands of pixles), $h(x_1,x_2)={\theta }_0+{\theta }_1{x}_1+{\theta }_2{x}_2$. We can see that this nomenclature pattern matches ${\theta }_k$ with $x_k$, and $x_0$ doesn't exist because ${\theta }_0$ is the affine parameter.

Our parameters can be stored in the vector $\theta =\left[\begin{array}{c}{\theta }_1\\ {\theta }_2\\ {\theta }_3\end{array}\right]$.

Our features can be stored in $x=\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]$.