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

A LASSO model minimizes the sum of squared residuals plus lambda times the sum of absolute coefficients. A model has coefficients 2.0, -1.5, 0.5 and 0 for four predictors. If lambda is increased substantially, which outcome is most likely, all else equal?

A larger lambda shrinks coefficients further and drives more of them exactly to zero, giving a simpler model. In-sample fit worsens because bias rises, while variance falls, which may help out-of-sample performance if the original model overfitted.

  1. ATraining sum of squared residuals falls and more coefficients become nonzero
  2. BCoefficients move away from zero and variance increases
  3. CCoefficients shrink further, more become exactly zero, and in-sample fit worsensCorrect
  4. DCoefficients are unchanged because lambda only affects the intercept

Explanation

A larger lambda raises the cost of large coefficients, so estimates shrink and small ones reach zero. The model becomes simpler, with higher bias, lower variance, and a higher in-sample sum of squared residuals.

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