Introduction

Regularization is a fundamental concept in machine learning that addresses the challenge of overfitting and improves the generalization ability of predictive models. In this chapter, we will delve into the importance of regularization and explore two widely used techniques: Ridge Regression and LASSO (Least Absolute Shrinkage and Selection Operator). These techniques play a crucial role in balancing model complexity and preventing overfitting, ensuring more reliable predictions on unseen data.

Need for Regularization

Overfitting occurs when a model learns to capture noise and random fluctuations in the training data, leading to poor performance on new, unseen data. Regularization techniques impose constraints on the model parameters, discouraging overly complex models that can fit noise. By controlling model complexity, regularization prevents overfitting and enhances the model’s predictive power.

Ridge Regression

Ridge Regression, also known as $L 2$ regularization, adds a penalty term proportional to the square of the magnitude of coefficients. This penalty term discourages large coefficient values, effectively shrinking them towards zero. The Ridge Regression cost function is given by:

$$\text { Cost }=\text { RSS }+ \alpha \Sigma\left(\beta^2\right)$$

Where RSS is the Residual Sum of Squares, $\beta$ is the coefficient vector, and $\alpha$ is the regularization parameter.

LASSO (Least Absolute Shrinkage and Selection Operator)

LASSO, an L1 regularization technique, introduces a penalty term proportional to the absolute values of coefficients. Unlike Ridge Regression, LASSO can drive some coefficients to exactly zero, leading to feature selection. The LASSO cost function is given by:

$$\text { Cost }=\text { RSS } + \alpha \Sigma \mid \beta \mid$$

Here, RSS, $\beta$, and $\alpha$ have the same meanings as in Ridge Regression.

Key Differences

• Ridge Regression tends to shrink coefficients smoothly, keeping all variables in the model but reducing their impact. It’s suitable when all features may contribute to the prediction.

• LASSO encourages sparsity in the coefficient vector, effectively performing feature selection by setting some coefficients to zero. It’s useful when there’s a belief that only a subset of features is relevant.

Example: Consider a housing price prediction model with multiple features like size, number of rooms, and location. If Ridge Regression is applied, all features are likely to be retained but with smaller impact. On the other hand, LASSO might identify that only size and location significantly affect prices, leading to a sparse model.