Linear Approximation

• Here's an introduction to machine learning.
• If you have a plot of points on a 2D chart.
• You can calculate a best fit line through them.
• This is linear approximation.
• If the line is a good fit, storing the line ax+by=c is a lot cheaper than storing say 100 points (or even 2).
• Given a y (or an x) you can calculate the x (or y).
• With the points, if you have the y, you can get the x.
• Without the line, how do you get an x if you don't have a y? (Nearest neighbor?)
• You can use linear regression to solve for a line, or other more sophisticated methods to derive more complex functions as approximators.
• One way to do it is to plot the points on a graph, and eye ball it (people are pretty good at this).
• Another way is to minimize the mean square error.
• If the mean error is small, it's a good fit.
• Look at the simple linear reqression wiki for a formula (that won't be on the exam).