Q.

Suppose we fit Lasso Regression to a data set, which has 100 features (X1,X2X100). Now, we rescale one of these feature by multiplying with 10 (say that feature is X1), and then refit Lasso regression with the same regularization parameter.Now, which of the following option will be correct?

A. it is more likely for x1 to be excluded from the model
B. it is more likely for x1 to be included in the model
C. can't say
D. none of these
Answer» B. it is more likely for x1 to be included in the model
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Discussion

Ashish Gautam
5 months ago

In this case, since you have multiplied X1 by 10, the penalty for X1 will be 10 times stronger than before during the Lasso Regression fitting. This stronger penalty makes it more likely for the coefficient of X1 to be shrunk towards zero. In other words, it is more likely for X1 to have a coefficient of exactly zero, effectively excluding it from the model.
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