Functional: introduction

This section focuses on implementinng the 1D Ridge problem using functions and Rust standard library only. It's divided into 5 subsections:

1. Loss function: Shows how to implement the Ridge loss function in two simple ways.
2. Closed-form solution: Implements the closed-form solution of the Ridge optimization problem.
3. Gradient-descent: Solves the Ridge problem using gradient descent to illustrate how to perform for loops.
4. Putting things together: Explains how to assemble everything into a simple library.
5. Exposing API: Explains how to use lib.rs to define what is made available to the user.

What we're building here

The aim of this chapter is to build a small crate with the following layout:

crates/ridge_1d_fn/
├── Cargo.toml
└── src
    ├── estimator.rs           # Closed-form solution of the Ridge estimator
    ├── gradient_descent.rs    # Gradient descent solution
    ├── lib.rs                 # Main entry point for the library
    └── loss_functions.rs      # Loss function implementations

It is made of three modules: estimator.rs, gradient_descent.rs, and loss_fnctions.rs. At the end of the chapter, we end up with a crate that can be used as follows:

use ridge_1d_fn::{fit, predict};

fn main() {
    let x = vec![1.0, 2.0, 3.0];
    let y = vec![2.0, 4.0, 6.0];

    let beta = fit(&x, &y, 0.1, 0.01, 1000, 0.0);
    let preds = predict(&x, beta);

    println!("Learned beta: {}", beta);
    println!("Predictions: {:?}", preds);
}

The fit and predict functions are implemented in the library entry point lib.rs.

Note that the gradient_descent.rs, and loss_fnctions.rs modules mostly serve as additional illustrations.

What's next

After this first chapter, we explore how to implement the same things using structs and traits to make our code more modular.