Here’s everything you need to know (beyond the standard definition) to master the numerical derivative world
There is a legendary statement that you can find in at least one lab at every university and it goes like this:
Theory is when you know everything but nothing works.
Practice is when everything works but no one knows why.
In this lab, we combine theory and practice: nothing works and nobody knows why
I find this sentence so relatable in the data science world. I say this because data science starts as a mathematical problem (theory): you need to minimize a loss function. Nonetheless, when you get to real life (experiment/lab) things start to get very messy and your perfect theoretical world assumptions might not work anymore (they never do), and you don’t know why.
For example, take the concept of derivative. Everybody who deals with complex concepts of data science knows (or, even better, MUST know) what a derivative is. But then how do you apply the elegant and theoretical concept of derivative in real life, on a noisy signal, where you don’t have the analytic…