Why regularisation matters in real regression problems
Linear regression can look deceptively simple: fit a line (or hyperplane) that minimises prediction error. In practice, datasets often contain many correlated inputs, noisy signals, and limited samples. Under these conditions, ordinary least squares can overfit—fitting random noise instead of stable patterns—leading to weak performance on new data.
Regularisation fixes this by adding a penalty term to the loss function. The model is still encouraged to fit the data, but it is also encouraged to keep coefficients “small” in a controlled way. This creates simpler, more generalisable models and reduces sensitivity to data quirks. If you are studying these trade-offs in a data scientist course in Delhi, understanding the L1 and L2 penalty behaviours is foundational for both modelling and interpretation.
The core idea: one loss, two different penalties
A regularised regression objective typically looks like this:
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Data fit term: mean squared error (MSE) between predictions and true values
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Penalty term: discourages large coefficients
The difference between Lasso and Ridge is the penalty form:
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Ridge (L2 norm): adds a penalty proportional to the sum of squared coefficients
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Lasso (L1 norm): adds a penalty proportional to the sum of absolute coefficients
These penalties reshape the optimisation landscape. That shape difference is what produces the practical differences you observe: sparsity, stability, and how models behave with correlated features.
L2 norm and Ridge: stability with correlated features
Ridge regression uses the L2 penalty. Squaring the coefficients means large weights are punished heavily, while small weights are penalised lightly. This creates a smooth optimization surface and tends to shrink all coefficients towards zero without forcing many of them to be exactly zero.
When Ridge is strong:
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Multicollinearity: If features are correlated (e.g., “total spend” and “number of purchases”), Ridge will distribute weight across them rather than arbitrarily picking one.
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Predictive focus: If the goal is stable prediction rather than feature selection, Ridge often performs well.
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Many small signals: In problems where many variables each contribute a little, Ridge preserves them in a controlled manner.
Intuition: Ridge prefers “many small effects” over “a few big effects.” That often improves generalisation, especially when the dataset has more features than you would ideally want in a linear model.
L1 norm and Lasso: sparsity and built-in feature selection
Lasso regression uses the L1 penalty. Because it penalises absolute values, it creates “corners” in the optimisation geometry. These corners make it more likely that the best solution lands exactly on an axis, meaning some coefficients become exactly zero.
What this gives you:
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Automatic feature selection: A coefficient of zero effectively removes a feature from the model.
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Simpler models: With fewer active predictors, explanations and deployment can be easier.
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Handling high-dimensional data: When you have many potential predictors (marketing tags, text-derived features, sensor variables), Lasso can help you reduce complexity.
But there is a trade-off: with strongly correlated predictors, Lasso can behave like a “winner-takes-most” method—often selecting one feature from a correlated group and dropping the others. That can be useful for simplification, but it can also make the chosen feature unstable across different samples.
This is one reason the L1 vs L2 comparison is emphasised in a data scientist course in Delhi: the penalty choice shapes both accuracy and interpretability.
Choosing between Lasso and Ridge in practice
A simple way to decide is to match the method to the data structure and your goal:
Choose Ridge when:
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You care primarily about predictive accuracy and stability.
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Many features are correlated and you want consistent coefficients.
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You expect many small contributions rather than a few dominant ones.
Choose Lasso when:
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You want a compact model with fewer predictors.
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Interpretability matters and you prefer a short list of key drivers.
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You suspect only a subset of variables truly matter.
Common workflow tip: Use both. Compare cross-validated performance, coefficient patterns, and stability across folds. In many real projects, the best model is not just the one with the lowest error, but the one that is robust and explainable.
Practical optimisation details that people often miss
Regularisation works best when the setup is correct:
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Standardise features. L1/L2 penalties depend on coefficient size, and coefficient size depends on feature scale. Without scaling, the penalty unfairly targets some variables.
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Tune the penalty strength (λ/alpha). Too little penalty behaves like plain regression; too much penalty underfits. Use k-fold cross-validation.
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Track both error and sparsity. A slightly higher error may be worth it if the model is far simpler and more stable to maintain.
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Consider Elastic Net when needed. Elastic Net blends L1 and L2, often giving a good balance: some sparsity plus better behaviour with correlated features.
These details matter in production pipelines, where the model needs to survive data drift and changing feature distributions—topics that typically follow after the basics in a data scientist course in Delhi.
Conclusion
Lasso (L1) and Ridge (L2) are not just minor variations; they reflect two different philosophies of modelling. L1 encourages sparsity and feature selection, producing simpler models but potentially unstable choices under correlation. L2 encourages smooth shrinkage and stability, usually improving generalisation when many predictors carry overlapping information. The best choice depends on whether you prioritise interpretability, feature reduction, coefficient stability, or pure predictive performance—and the most reliable approach is to validate the decision using scaled inputs and cross-validated tuning in your actual dataset.
