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FRM Part I · FRM Exam Part I · Machine-Learning Methods

A risk team chooses the penalty parameter lambda for an Elastic Net model using k-fold cross-validation. Which description of the procedure and rationale is correct?

Choose the lambda that gives the lowest average error on the held-out validation folds in cross-validation. This approximates out-of-sample performance and balances bias against variance. Minimizing in-sample error would pick no penalty and overfit, while an excessively large lambda would underfit.

  1. ASelect the lambda that minimizes the in-sample residual sum of squares, since this gives the best fit
  2. BSelect the lambda with the lowest average validation-fold error, because it estimates out-of-sample performanceCorrect
  3. CSelect the largest lambda available, because more shrinkage always improves forecasting
  4. DSelect lambda = 0, because Elastic Net is unbiased only when no penalty is applied and this ensures optimal prediction

Explanation

In-sample RSS is minimized at lambda = 0, which risks overfitting. Cross-validation repeatedly fits on training folds and measures error on held-out folds; the lambda with the lowest average validation error is chosen to balance bias and variance. Too large a lambda causes underfitting.

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