Which Regularizer Should You Actually Use? Lessons from 134,400 Simulations

This article presents a decision framework for choosing between Ridge, Lasso, and ElasticNet regularizers in machine learning models, based on three quantities that can be computed before fitting the model. The framework is derived from an analysis of 134,400 simulations, providing a data-driven approach to regularizer selection.

⚡ Key Takeaways

• The decision framework considers three quantities: the L1 ratio, the L2 ratio, and the L1-L2 ratio.
• The L1 ratio is the ratio of the L1 norm of the coefficients to the L2 norm, while the L2 ratio is the ratio of the L2 norm to the L1 norm.
• The L1-L2 ratio is the ratio of the L1 norm to the L2 norm.
• Ridge regression is preferred when the L2 ratio is high, while Lasso regression is preferred when the L1 ratio is high.
• ElasticNet regression is preferred when the L1-L2 ratio is high.

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