I recently learned about a cool way to minimize functions (like the true mathie I am!) and that way is through Gradient Descent. It’s a method, that I personally was never taught in my Math degree, to analyse the classic linear regression problem.
Here’s how it works: say you have a function that is defined by some set of parameters (for example, a typical cost function). If you start at some initial value on that function, Gradient Descent will take “baby steps” (defined by you), iteratively, towards a set of parameters that minimize the function. This happens through the magical methods of calculus! More specifically, “stepping” proportional to the negative of the Gradient of the function at the initial value.
You can also have some fun by using your favourite coding method (Octave is free software that is similar to Matlab that is good for beginners!) and implement the following: