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

A LASSO regression with a single standardized predictor minimizes the sum of squared residuals plus lambda times the absolute value of the coefficient. When the penalty is increased from a very small value to a very large value, which outcome is most likely for the coefficient and the model?

The coefficient shrinks toward zero and eventually becomes exactly zero. A larger LASSO penalty makes the model simpler, which raises bias but lowers variance. The exact-zero outcome arises from the L1 penalty's kink at zero, unlike ridge, where coefficients approach but do not reach zero.

  1. AThe coefficient moves toward zero and eventually equals exactly zero, increasing bias while reducing varianceCorrect
  2. BThe coefficient grows larger in magnitude, reducing bias and increasing variance
  3. CThe coefficient stays unchanged because the penalty affects only the intercept
  4. DThe coefficient moves toward zero but never reaches it, as in ridge regression

Explanation

Raising lambda in LASSO increases the cost of nonzero coefficients. Because the L1 penalty has a kink at zero, the coefficient reaches exactly zero for large enough lambda. The model becomes simpler, with higher bias and lower variance. The last option describes ridge, not LASSO.

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