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When is Elastic Net better than pure Lasso or Ridge?

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Answer

  • Elastic Net combines L1 and L2 penalties: α    (ρ    w1  +  (1ρ)    0.5    w22)\alpha\; \cdot \;(\rho\; \cdot \; \mid w \mid 1\; + \;(1 - \rho)\; \cdot \;0.5\; \cdot \; \mid w \mid 2^{2}).
  • Use it when (1) features are highly correlated — Lasso arbitrarily picks one and drops the rest, Elastic Net groups correlated features together via the L2 term; (2) you have more features than samples (p >> n) — Lasso caps the number of selected features at n.
  • Tune rho on validation data.
Check yourself — multiple choice
  • Elastic Net always equals Ridge
  • It combines L1 and L2, handling correlated features and p >> n better than pure Lasso
  • It only works for classification
  • It replaces cross-validation

Elastic Net = L1 + L2. Better than Lasso when features are correlated or p >> n.

#regularization#linear-models

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