Little Bits of Artificial Intelligence

1. What is ElasticNet Regression?

ElasticNet Regression is a smart combination of two popular techniques used to improve linear regression:

• Ridge Regression (L2 Regularization): Shrinks all coefficients but does not eliminate any.
• Lasso Regression (L1 Regularization): Can eliminate less important features (i.e., set their weights to zero).

ElasticNet = Lasso + Ridge

It balances the strengths of both:

• It shrinks coefficients to avoid overfitting (like Ridge)
• It can remove unimportant features (like Lasso)

This is useful when:

• We have lots of features (possibly more than data points)
• Some of those features are highly correlated
• We want both model simplicity and prediction accuracy

Simple Formula:

ElasticNet minimizes:

Loss=RSS+λ1∑∣βi∣+λ2∑βi2

Where:

• RSS = residual sum of squares (error)
• λ₁ controls Lasso part (L1 penalty)
• λ₂ controls Ridge part (L2 penalty)

2. Real Life Examples

A. House Price Prediction

Imagine we’re predicting house prices based on:

• Area, number of bedrooms, bathrooms, distance to city, type of flooring, garden size, wall color, etc.

Problem:

• Some features are correlated (e.g., area and number of bedrooms)
• Some are irrelevant (e.g., wall color)

ElasticNet helps:

• Reduce weights for correlated ones without overfitting
• Remove wall color as it’s not useful

B. Genetics & Health Prediction

In medical research, we might want to predict the likelihood of a disease based on thousands of genetic markers (genes).

Problem:

• Many markers may not matter
• Some are highly correlated due to gene clusters

ElasticNet helps:

• Ignore irrelevant genes
• Handle gene groups that work together
• Avoid overfitting by regularizing complex models