Math for Programmers

14 Fitting functions to data

This chapter covers

• Measuring how closely a function models a data set
• Exploring spaces of functions determined by constants
• Using gradient descent to optimize the quality of “fit”
• Modeling data sets with different kinds of functions

The calculus techniques you learned in part 2 require well-behaved functions to be applicable. For a derivative to exist, a function needs to be sufficiently smooth, and to calculate an exact derivative or integral, you need a function to have a simple formula. For most real-world data, we aren’t so lucky. Due to randomness or measurement error, we rarely come across perfectly smooth functions in the wild. In this chapter, we cover how to take messy data and model it with a simple ...