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

A analyst compares penalized regressions on a data set with many correlated predictors, some of which are believed to be irrelevant. She wants a method that can set some coefficients exactly to zero, performing variable selection. Which statement is correct?

LASSO can set coefficients exactly to zero because its L1 penalty on the sum of absolute coefficients creates corner solutions, giving variable selection. Ridge uses a squared (L2) penalty that shrinks coefficients toward zero but generally leaves all predictors in the model.

  1. ARidge regression sets coefficients exactly to zero because it penalizes squared coefficients
  2. BLASSO can set coefficients exactly to zero because it penalizes the sum of absolute coefficient valuesCorrect
  3. CBoth ridge and LASSO always keep every predictor in the model
  4. DNeither method can reduce the number of predictors

Explanation

LASSO uses an L1 penalty (sum of absolute values), whose geometry produces corner solutions with some coefficients exactly zero. Ridge uses an L2 penalty, which shrinks coefficients toward zero but typically not exactly to zero, so option A is wrong.

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