Why Is the L1 Norm Less Sensitive to Outliers Compared to L2 Norm?

Discover why the L1 norm is less sensitive to outliers by minimizing absolute errors instead of squared errors for more robust models.

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L1 norm, or least absolute deviations, is less sensitive to outliers because it minimizes the sum of absolute errors rather than squared errors. Outliers have a disproportionate influence on the L2 norm (least squares) by squaring the deviations, which significantly amplifies the impact of large errors. In contrast, L1 treats all errors equally by focusing on their absolute values, resulting in a more robust model in the presence of outliers.

FAQs & Answers

  1. What is the main difference between L1 and L2 norms in regression? The L1 norm minimizes the sum of absolute errors, making it less sensitive to outliers, while the L2 norm minimizes the sum of squared errors, which amplifies the effect of large deviations.
  2. Why are outliers problematic in least squares regression? Outliers have a disproportionate influence in least squares regression because the error is squared, which significantly increases their impact on the model's fit.
  3. When should I use L1 norm over L2 norm? Use the L1 norm when you want a model that is more robust to outliers or when you expect your dataset to include anomalies that could skew model performance.

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