Machine learning / Feature selection (LASSO)
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LASSO adds an L1 penalty λ·Σ|coefficient| to linear regression: the larger λ, the more coefficients are shrunk to exactly 0; the rest are the selected features. Each feature is first standardised (mean 0, SD 1) so the penalty treats them equally.
The first chart shows the cross-validated error (±1 SE) for each λ: the “minimum” rule takes the lowest point; the “one-standard-error” rule takes the largest λ whose error is within one SE of the minimum, giving fewer and more stable features.
The second chart is the coefficient path: reading from right (large λ) to left, features that leave 0 earlier matter more; “entry_step_on_path” in the table gives the step at which each feature enters.
Among highly correlated features LASSO tends to keep only one; a feature shrunk to 0 is not necessarily unrelated to the outcome. With few samples the selection varies with the fold split, so try another seed to check stability.
The selected-feature table gives standardised and original-unit coefficients; CV R² = 1 − cross-validated MSE / outcome variance.
Tibshirani (1996) J R Stat Soc B 58:267–288; solved by coordinate descent (Friedman et al. 2010, J Stat Softw 33:1); the objective 1/(2n)·||y − Xβ||² + λ||β||₁, λ grid and k-fold choice match scikit-learn LassoCV; the one-standard-error rule follows Hastie et al., The Elements of Statistical Learning.
Runs in your browser: up to roughly 2 million sample × feature cells (e.g. 500 × 4,000) is recommended.
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