L1 Regularization
Definition
L1 regularization adds the sum of the absolute parameter values to the objective function.
It can shrink weights exactly to zero, promoting sparse models or feature selection. The effect depends on scaling and regularization strength.
Simply explained
Like a penalty for many or large weights, which can push some weights exactly to zero.
Why it matters in practice
Relevant for linear models, feature selection, and sparse modeling.
Example from business
A linear model uses L1 regularization to obtain a sparser set from many correlated features.
Limits and pitfalls
- Do not scale features; do not automatically interpret zero coefficients as causal; choose regularization based on test data.
Origin & history
Tibshirani introduced the Lasso as an L1-based regression method in 1996.
Use in mid-sized companies
- Possible application in SMEs: Evaluate sparse models when many potential features exist.
Frequently asked questions
Does L1 always produce sparse models?
Often, but depends on data and strength. Is L1 the same as L2? No.
Sources
- Regression Shrinkage and Selection via the Lasso · Tibshirani (1996), Regression Shrinkage and Selection via the Lasso
Sources checked on 10.10.2026.
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