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From my understanding, Ridge regression tends to shrink coefficients towards 0 as lambda increases. However, it seems this is not always the case - for features which are more statistically significant, Ridge Regression can increase their coefficient as lambda increases. Why is this? And how does the Ridge penalty cause this?

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  • $\begingroup$ A related question is stats.stackexchange.com/questions/414088 would my answer there answer your question here? "The ridge path is not a straight line ... Shrinking the parameters in a straight line from the OLS solution to 0, means that the sum of squared error becomes high. Taking a detour allows to shrink the parameters with less reduction of the sum of least squared error." $\endgroup$
    – Sextus Empiricus
    Commented Nov 17, 2022 at 7:36

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