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FRM Part I · FRM Exam Part I · Machine Learning and Prediction

A risk analyst fits a linear model to predict loan losses using 60 correlated explanatory variables and only 120 observations. The analyst wants a method that shrinks coefficients toward zero but never sets any coefficient exactly to zero. Which approach fits this requirement?

Ridge regression with an L2 penalty fits the requirement. It shrinks coefficients toward zero by penalizing their squared sum, but with a finite penalty it never sets them exactly to zero. LASSO, using an L1 penalty, can eliminate variables entirely, so it does not meet the stated need.

  1. ARidge regression with an L2 penaltyCorrect
  2. BLASSO regression with an L1 penalty
  3. COrdinary least squares with no penalty
  4. DBest subset selection

Explanation

Ridge adds a penalty on the sum of squared coefficients (L2). This shrinks coefficients smoothly toward zero but, for a finite penalty, does not set them exactly to zero. LASSO's L1 penalty can set coefficients exactly to zero, so it performs variable selection and does not meet the requirement.

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