Lasso Regression – Machine Learning Practice

2026 • Suraj Singh
Data Science

date: 2026-03-04

Lasso Regression – Machine Learning Practice

This repository contains my practice and notes for Lasso Regression, part of my daily Machine Learning learning series where I study and implement one algorithm at a time.

What is Lasso Regression?

Lasso Regression (Least Absolute Shrinkage and Selection Operator) is a linear regression technique that uses L1 regularization to reduce overfitting and perform automatic feature selection.

It works by adding a penalty to the loss function which shrinks coefficients. Some coefficients may become exactly zero, effectively removing those features from the model.

Mathematical Formula

Linear Regression minimizes:

[ RSS = \sum (y - \hat{y})^2 ]

Lasso adds an L1 penalty:

[ Loss = RSS + \lambda \sum |\beta| ]

Where:

  • RSS = Residual Sum of Squares
  • β = Model coefficients
  • λ (lambda / alpha) = Regularization strength

Key Idea

As λ increases:

  • Coefficients shrink
  • Some coefficients become 0
  • Irrelevant features are removed from the model

This helps create a simpler and more interpretable model.

Lasso Path (Coefficient Shrinking)

The Lasso Path graph shows how coefficients change as regularization strength increases.

  • Small λ → behaves like Linear Regression
  • Medium λ → coefficients shrink
  • Large λ → some coefficients become 0

This demonstrates feature selection in Lasso Regression.

Dataset

A synthetic dataset was generated using sklearn.make_regression with:

  • 1200 rows
  • 20 features
  • 5 informative features
  • Remaining features are noise

This helps clearly demonstrate how Lasso removes irrelevant features.

Implementation Steps

  1. Generate synthetic dataset
  2. Split dataset into training and testing sets
  3. Apply feature scaling using StandardScaler
  4. Train Lasso Regression model
  5. Analyze coefficients
  6. Visualize Lasso coefficient path

Technologies Used

  • Python
  • NumPy
  • Pandas
  • Matplotlib
  • Scikit-learn

Learning Outcome

Through this practice I understood:

  • L1 Regularization
  • Overfitting and regularization
  • Feature selection using Lasso
  • Effect of lambda (α) on coefficients
  • Lasso coefficient shrinking path

Machine Learning Series

This project is part of my daily Machine Learning practice series where I learn and implement ML algorithms step by step.

Algorithms covered so far:

  • Linear Regression
  • Ridge Regression
  • Lasso Regression

More algorithms coming soon.

Connect With Me

If you are also learning Machine Learning, feel free to connect and follow my journey.

If you want the notes or notebook used in this project, reach out and I'll share them.

Happy Learning 🚀