Summary – Lasso Regression

1. Start with the Data

  • Collect a dataset with input features (X) and target values (y).
  • Example:
    House Price=f(Area,Rooms,Plants,…)

2. Define the Model

  • Use a linear equation to predict the target:
    y^=w1x1+w2x2+⋯+wnxn+b
  • Here, w1,w2,…,wn are weights (importance of each feature).

3. Measure Prediction Error

  • Use Mean Squared Error (MSE) to see how wrong the predictions are:

4. Add L1 Penalty (Lasso Regularization)

  • Add a cost for using features:

  • λ (lambda) controls how strict the penalty is:
    • Higher λ → more features pushed to zero
    • Lower λ → behaves more like normal linear regression

5. Optimize (Train the Model)

  • Use gradient descent or similar methods to:
    • Minimize the loss
    • Update weights wjw_jwj​ and bias bbb
    • Apply L1 penalty so that some weights shrink to zero

6. Drop Useless Features

  • After training:
    • Important features keep non-zero weights.
    • Less useful ones are automatically removed (set to zero).

7. Final Model = Simple + Accurate

  • The final model uses only the most relevant features.
  • Helps with:
    • Feature selection
    • Model simplicity
    • Avoiding overfitting

One-line Summary:

Lasso Regression = Linear Regression + Penalty for Using Too Many Features

It rewards simplicity by shrinking unnecessary features to zero, making our model cleaner and easier to understand.

Next – Elasticnet Regression