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

A risk analyst fits a linear model to predict loan losses using 60 correlated predictors and finds that many coefficients are very large with opposing signs, producing poor out-of-sample performance. She adds a penalty equal to lambda times the sum of squared coefficients to the least-squares objective. Which statement best describes the effect of this penalty?

The squared-coefficient penalty is ridge regularization. It shrinks coefficients toward zero, which lowers variance at the cost of added bias, but it generally does not set coefficients exactly to zero. Exact zeros and variable selection are features of the LASSO absolute-value penalty.

  1. AIt shrinks coefficients toward zero but does not typically set any of them exactly to zeroCorrect
  2. BIt sets many coefficients exactly to zero, performing automatic variable selection
  3. CIt removes the bias of the coefficient estimates by rescaling them
  4. DIt increases the variance of the estimates in exchange for lower bias

Explanation

A penalty on the sum of squared coefficients is ridge (L2) regularization. It shrinks coefficients smoothly toward zero, reducing variance at the cost of some bias, but rarely produces exact zeros. LASSO, with an absolute-value penalty, is the method that performs variable selection.

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