Certainly! Here are the key differences between Lasso regression and Ordinary Least Squares (OLS) regression:
Ordinary Least Squares (OLS) Regression:
- Objective: OLS aims to minimize the sum of the squared differences between the observed values and the predicted values (the residuals).
- Coefficients: OLS does not impose any constraints on the coefficients, which means it can produce non-sparse solutions. All features can have non-zero coefficients.
- Overfitting: OLS can be prone to overfitting, especially when there are many features relative to the number of samples, as it tries to fit the training data as closely as possible.
- Interpretability: Since OLS includes all features, it may be harder to interpret the model when many features are present.
Lasso Regression:
- Objective: Lasso (Least Absolute Shrinkage and Selection Operator) also aims to minimize the sum of squared differences, but it adds a penalty equal to the absolute value of the coefficients (L1 regularization).
- Coefficients: Lasso encourages sparsity in the model by shrinking some coefficients to exactly zero, effectively performing feature selection. This means it can exclude irrelevant features from the model.
- Overfitting: The penalty term helps to reduce overfitting by discouraging overly complex models, making Lasso more robust in high-dimensional settings.
- Interpretability: Lasso can lead to simpler models with fewer features, making it easier to interpret the results.
Summary:
In summary, while both OLS and Lasso regression aim to model the relationship between features and a target variable, Lasso includes a regularization term that promotes sparsity and can help prevent overfitting, making it particularly useful in scenarios with many features.
