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134,400 Simulations Reveal Best Regularizer

To determine the most effective regularization method for machine learning, researchers Ahsaas Bajaj and Benjamin S Knight of Instacart conducted 134,400 simulations based on eight real-world production models. Their study benchmarks four regularization frameworks—Ridge, Lasso, ElasticNet, and Post-Lasso OLS—across three objectives: predictive accuracy, variable selection, and coefficient estimation. The results reveal that the optimal choice depends on the sample-to-feature ratio and the condition number of the data matrix, with sample size being the single most critical factor for overall performance. For predictive accuracy measured by test RMSE, the study found that Ridge, Lasso, and ElasticNet are nearly interchangeable, with differences in median error rarely exceeding 0.3%. Because Ridge offers a closed-form solution that is significantly faster—taking roughly 6 seconds compared to 48 seconds for ElasticNet in many cases—it is the recommended default for prediction tasks. While ElasticNet can outperform Ridge in very specific low-sample, high-signal scenarios, the marginal gain rarely justifies the computational overhead. Variable selection, however, requires a more nuanced approach. ElasticNet emerges as the safest default, particularly when features exhibit high multicollinearity (a condition number greater than 10,000). In these common production scenarios, Lasso tends to arbitrarily select one feature from a correlated group and discard the rest, severely compromising recall. ElasticNet mitigates this through its L2 penalty, which groups correlated features together and maintains high recall regardless of the signal-to-noise ratio. Even in well-conditioned datasets with low multicollinearity, Lasso remains risky unless the practitioner knows with certainty that the true model is sparse and the signal is strong. Ridge can achieve high F1 scores in low-sample regimes by retaining all features, but this does not constitute genuine variable selection. Regarding coefficient estimation, which is vital for interpretability and causal inference, the decision branches on the condition number. At high multicollinearity, ElasticNet consistently outperforms other methods by achieving 20% to 40% lower L2 error. At low multicollinearity, the optimal method depends on the sparsity of the true coefficients, a factor often unknown in advance. The study strongly advises against Post-Lasso OLS, which refits unpenalized coefficients after variable selection, as this procedure amplifies first-stage selection errors and yields higher coefficient error across all tested regimes. The researchers distilled these findings into a practical decision framework. If the ratio of samples to features exceeds 78, method choice becomes irrelevant, and practitioners should default to the computationally efficient RidgeCV. When the sample-to-feature ratio is below 78, the condition number becomes the primary guide. For high multicollinearity, ElasticNetCV is the superior choice. For well-conditioned data, ElasticNet remains a safe default, though Lasso becomes viable if domain expertise confirms sparsity and signal strength. To assess the latent signal-to-noise ratio without prior knowledge, the regularization strength selected by a quick LassoCV run can serve as a proxy. Ultimately, the study concludes that increasing the sample-to-feature ratio has a far greater impact on model performance than any specific regularizer choice. Practitioners should focus their resources on data collection rather than extensive hyperparameter tuning, using the derived decision guide only when sample sizes are limited.

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134,400 Simulations Reveal Best Regularizer | Trending Stories | HyperAI