Regularized Regression

regularized-regression

Fits Ridge, Lasso, or ElasticNet regression with cross-validated alpha selection. Produces a structured RegularizedRegressionReport (JSON + HTML) with a regularisation path, CV curve, feature selection summary, and OLS comparison.

When to use

• Your pre-analysis flags HIGH_VIF (multicollinearity) → try Ridge or ElasticNet.
• You have many features and expect a sparse signal → try Lasso.
• You want automatic feature selection with grouping of correlated predictors → use ElasticNet.
• Your OLS standard errors are unreliable due to collinearity → regularisation stabilises estimates.

Quick start

# Lasso (default) — auto-selects alpha via 5-fold CV
python .agents/skills/regularized-regression/scripts/fit.py \
  --data data.csv \
  --target price \
  --features sqft,bedrooms,bathrooms,location \
  --output out/lasso \
  --dataset-name "Housing data"

# Ridge — good when all features plausibly contribute
python .agents/skills/regularized-regression/scripts/fit.py \
  --data data.csv --target y --features all \
  --method ridge --output out/ridge

# ElasticNet — multicollinear groups + sparse signal
python .agents/skills/regularized-regression/scripts/fit.py \
  --data data.csv --target y --features all \
  --method elasticnet --l1-ratio 0.7 --output out/enet

Arguments

Outputs

out/
├── report.json   # RegularizedRegressionReport (Pydantic schema)
└── report.html   # Self-contained HTML with Plotly charts

Report sections

• Fit summary — R², adj. R², residual SE, selected α
• Coefficients — table + forest plot (non-zero features, sorted by |β|)
• Regularisation path — coefficient trajectories over the full α grid
• Cross-validation — CV R² curve with ±1 SD band and selected-α markers
• Interpretation — one plain-language fact per non-zero coefficient
• Feature selection (Lasso/ElasticNet only) — retained vs. zeroed features
• OLS comparison — side-by-side coefficient table and R² comparison
• Flags & recommendations

Notes

• Features are standardised before fitting; coefficients in the report are on the original scale.
• SE, CI, and p-values are approximate (derived from OLS). They are presented for orientation only — regularised estimators are biased, so classical frequentist inference does not strictly apply.
• Ridge never zeros coefficients; feature_selection is null for ridge.

References

• references/regularization_choice.md — When to pick Ridge vs. Lasso vs. ElasticNet
• references/cv_strategies.md — How cross-validation and alpha selection rules work