## Motivation

I have had the opportunity to work with various machine learning libraries on a variety of projects both for fun (See: hedgie-finder series) as well as with various research projects that I’ve been able to be a part, largely around using Deep learning for image noise removal and segmentation. While these projects helped familiarize myself with these libraries (fastai/pytorch and Tensorflow 1 respectively) as well as made me dig into the domain specific research practices, there remained many black-box elements that I wanted to better understand.

This series and others like it are for me to build up intuition by solving these small problems using a few different approaches with a focus on the more general methodology rather than on the specifics of any one library.

## A basic regression example

One such problem inspired by chapter 4 of Chris Mattman’s book Machine Learning with Tensorflow 2nd Edition is on fitting a model to continuous data, regressio. I followed along with his tutorial on using regression to model the call volume of New York City’s 311 service. I attempted using a newer 2019 dataset than the 2014 one used in the book and was not able to reproduce the results well, which perplexed me and made we want to dig in deeper into regression, which I’d already explored some in my interpolation tutorials, however this time I want to dig in more to iterative methods, the kind made famous by deep learning and related techniques.

Rather than get bogged down in the implementation details of a single library I worked through a derived line fitting example using two different machine learning libraries: Flux.jl and Tensorflow 2. Links to both of these tutorials can be found below:

I like the Vandermonde matrix polynomial solution because it is intuitive to me that anything can be approximated by a polynomial, this is the basis for Taylor Series. More detail on Vandermonde matrix methods can be found in this past series of posts: Vandermonde Interpolation.

Why not always use linear algebra type solutions? Vandermonde works great for small problems where the number of data instances is $N < 100$ or so. However when the number instances required number of monomial terms grows this Vandermonde matrix becomes large and cannot be inverted accurately. It’s in these big data regime domains (especially in imaging!) that these iterative techniques have proven to be powerful and why I want to learn more! Enjoy these posts as I explore these libraries to get started with regression.