Regularisation Path Results
Dataset Input
Model and Columns
Regularisation Path Settings
Preprocessing, Solver, and Validation
Chart Customisation
Formula Used
minimize (1 / 2n) Σ(yᵢ − β₀ − xᵢβ)² + λ Σ|βⱼ|
minimize (1 / 2n) Σ(yᵢ − β₀ − xᵢβ)² + λ Σβⱼ²
minimize (1 / 2n) Σ(yᵢ − β₀ − xᵢβ)² + λ[ρΣ|βⱼ| + (1 − ρ)Σβⱼ² / 2]
How to Use
Paste a numeric dataset or load an example. Parse the data, then choose the target and predictor columns. Review warnings before starting the full calculation.
Select Lasso, Ridge, or Elastic Net. Set the lambda range, spacing, solver tolerance, scaling, and cross-validation choices. Use logarithmic spacing for wide regularisation ranges.
Calculate the path and inspect coefficient shrinkage. Review validation curves, selected lambda, active features, and exported tables. Compare stable paths before choosing predictors.
Example Data Format
| size | bedrooms | age | distance | price |
|---|---|---|---|---|
| 1200 | 2 | 18 | 7.5 | 210 |
| 1650 | 3 | 10 | 5.2 | 295 |
| 2100 | 4 | 7 | 3.1 | 385 |
Frequently Asked Questions
What does a regularisation path show?
It shows each coefficient across changing penalty strengths. Shrinking paths reveal sensitivity and feature importance. Zero coefficients indicate excluded predictors.
Why should predictors be standardised?
Penalties act directly on coefficient sizes. Different predictor scales can distort comparisons. Standardisation creates a fairer regularisation path.
How does Lasso differ from Ridge?
Lasso can force coefficients exactly to zero. Ridge usually shrinks coefficients without removing them. Their paths therefore display different sparsity behaviour.
What does the Elastic Net ratio control?
It blends L1 and L2 penalties. A value near one resembles Lasso. A value near zero resembles Ridge.
Why use logarithmic lambda spacing?
Useful penalty values often span several magnitudes. Logarithmic spacing samples this range efficiently. It reveals both strong and weak shrinkage.
What is the minimum-error lambda?
It produces the best average validation score. It may retain more active predictors. Use it when prediction quality dominates simplicity.
What is the one-standard-error rule?
It chooses a simpler model near optimum. The selected score remains statistically competitive. It often improves interpretability and stability.
Why can correlated predictors swap importance?
Correlated variables carry overlapping information. Penalties can distribute or alternate their coefficients. Interpret groups instead of isolated path positions.
What causes convergence warnings?
The solver may need more iterations. Extreme scales or collinearity can slow optimisation. Increase iterations or standardise the predictors.