Start by identifying the core problem: with more predictors than observations, the model is overparameterized and prone to overfitting. Explain why this happens (multicollinearity, high variance, non-unique solutions) and then describe how L1 regularization addresses it by adding a penalty that drives some coefficients to zero, effectively performing feature selection and reducing variance.
Pro tip: Mention that L1 regularization yields sparse solutions, which is particularly useful when you suspect only a subset of the 500 predictors are relevant. Also, note that while L1 helps with overfitting, it introduces bias, so cross-validation is essential to tune the regularization strength.
State that with 500 predictors and 600 observations, the model is likely to overfit due to high dimensionality relative to sample size. This leads to poor generalization on unseen data.
Discuss the curse of dimensionality: with many predictors, the design matrix may be ill-conditioned or singular, causing multicollinearity and unstable coefficient estimates. The model has enough flexibility to fit noise, resulting in high variance.
Describe L1 regularization (Lasso) as adding a penalty equal to the absolute value of coefficients to the loss function. This constrains the coefficients and encourages sparsity by shrinking some to exactly zero.
L1 regularization performs feature selection by zeroing out irrelevant predictors, reducing model complexity and variance. It also helps with multicollinearity by selecting one predictor among correlated ones, leading to a more interpretable and generalizable model.
Mention that the regularization strength (lambda) must be tuned via cross-validation. Also note that L1 introduces bias but can significantly reduce variance, improving test performance.
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