Regularization Techniques: Ridge and Lasso Regression

These flashcards cover the key concepts of Ridge and Lasso regression as discussed in the lecture, focusing on their purposes, mechanics, and differences.

What is the purpose of regularization techniques like Ridge regression?

To reduce overfitting by introducing bias, which decreases variance in model predictions.

What does the Ridge regression penalty involve?

It adds a term lambda times the slope squared to the sum of squared residuals.

How does Ridge regression affect the slope when increasing the lambda value?

As lambda increases, the slope decreases and approaches zero, making predictions less sensitive.

What is one key difference between Ridge regression and Lasso regression?

Lasso regression can reduce coefficients to exactly zero, effectively removing variables from the model.

How is lambda determined in both Ridge and Lasso regression?

Lambda is determined using cross-validation, typically through 10-fold cross-validation.

What happens to the model when using Ridge regression with a small dataset?

It improves predictions by reducing the sensitivity of the predictions to the training data.

In what scenario would you prefer Lasso regression over Ridge regression?

When there are many variables present, some of which may be useless, Lasso can exclude them.

What is the outcome of Ridge regression on the model parameters in relation to their values?

Ridge regression shrinks parameters but never reduces them to zero.

What is the model objective in Ridge regression?

To minimize the sum of squared residuals plus the Ridge regression penalty.

What type of data can Ridge regression be applied to?

Both continuous and discrete variables, as seen with diet types predicting size.

What is the purpose of regularization techniques like Ridge regression?

To reduce overfitting by introducing bias, which decreases variance in model predictions.

What does the Ridge regression penalty involve?

It adds a term lambda times the slope squared to the sum of squared residuals.

How does Ridge regression affect the slope when increasing the lambda value?

As lambda increases, the slope decreases and approaches zero, making predictions less sensitive.

What is one key difference between Ridge regression and Lasso regression?

Lasso regression can reduce coefficients to exactly zero, effectively removing variables from the model.

How is lambda determined in both Ridge and Lasso regression?

Lambda is determined using cross-validation, typically through 10-fold cross-validation.

What happens to the model when using Ridge regression with a small dataset?

It improves predictions by reducing the sensitivity of the predictions to the training data.

In what scenario would you prefer Lasso regression over Ridge regression?

When there are many variables present, some of which may be useless, Lasso can exclude them.

What is the outcome of Ridge regression on the model parameters in relation to their values?

Ridge regression shrinks parameters but never reduces them to zero.

What is the model objective in Ridge regression?

To minimize the sum of squared residuals plus the Ridge regression penalty.

What type of data can Ridge regression be applied to?

Both continuous and discrete variables, as seen with diet types predicting size.

What is the mathematical expression for the Ridge regression penalty term?

\lambda \sum{j=1}^{p} \betaj^2 where \lambda \ge 0 and \beta_j are the regression coefficients.

What is the mathematical expression for the Lasso regression penalty term?

\lambda \sum{j=1}^{p} |\betaj| where \lambda \ge 0 and \beta_j are the regression coefficients.

How does regularization, specifically Ridge and Lasso, address the bias-variance trade-off?

By adding bias to the model (through the penalty term), regularization reduces the model's variance, thereby making predictions less sensitive to the training data and improving generalization.

What happens to the model coefficients in Ridge regression if the lambda value is set to zero?

When \lambda = 0 , the Ridge regression penalty term becomes zero, and the model is equivalent to ordinary least squares (OLS) regression, meaning the coefficients are not shrunk.

What regularization technique is associated with L2 regularization?

Ridge regression uses L2 regularization, which involves squaring the magnitudes of the coefficients.