Lasso Regularization

How Lasso Regularization Works

Lasso regularization adds an L1 penalty to a regression objective, so the model is optimised for both fit and simplicity. As coefficients are penalised, smaller ones are pushed toward zero, which makes the model easier to interpret and can remove weak predictors rather than merely shrinking them.

That zeroing effect is what distinguishes lasso from many other shrinkage methods. In practice, it means the model is not just trying to reduce variance from overfitting, but is also deciding which features are worth retaining. The trade-off is that useful predictors can be removed when the penalty is too strong or when features carry overlapping information.

Why Lasso Is Used

Lasso is often chosen when a dataset has many candidate variables and only some are expected to matter. It can improve generalisation by limiting model complexity, and it can also help reveal which inputs are carrying the signal. That makes it useful in settings where a smaller feature set is operationally easier to review, explain, or deploy.

Its feature-selection behaviour is especially valuable when a practitioner wants a compact linear model without building a separate variable-selection step. However, lasso is still a modelling choice, not a guarantee of true importance, because correlated predictors can cause the penalty to select one variable and suppress others that are equally informative.

Key Assumptions and Limitations

Lasso works best when the relationship between predictors and outcome is reasonably compatible with a linear model. It also assumes the regularisation strength has been chosen carefully, usually through validation. If the penalty is too weak, the model may still overfit; if it is too strong, it can underfit and discard signals that matter.

Another practical limitation is its behaviour with correlated features. When variables overlap strongly, lasso may select one representative feature while shrinking the rest to zero, even though the discarded variables still contain relevant information. In those cases, the selected set should be treated as a modelling result, not as a definitive causal ranking.

Where Lasso Fits in Model Building

Lasso sits within the broader family of regularised regression methods, alongside approaches such as ridge regression and elastic net. It is most useful when sparsity is an advantage and the goal is to balance predictive performance with a simpler coefficient structure. The method is common in exploratory analytics, baseline modelling, and situations where interpretability matters.

For a practical example, lasso can be helpful in high-dimensional settings where many features are noise, duplicated signals, or weak contributors. It gives practitioners a principled way to compress the model while keeping the regularisation logic inside the training process rather than adding manual pruning after the fact.

Related resources from NHI Mgmt Group

• L2 Regularization