Regression¶

Regression illustration: scattered observations with a fitted functional coefficient and prediction band

Predict, classify, and explain with functional predictors and responses.

The Regression module covers the full spectrum of supervised learning with functional data -- from classical scalar-on-function models to elastic regression, classification, conformal prediction, and model explainability.

Scalar-on-Function

FPC linear, PLS, and nonparametric regression with a scalar response.

Function-on-Scalar

FOSR and FANOVA for predicting functional responses.

Classification

LDA, QDA, k-NN, and kernel classifiers with cross-validation.

Elastic Regression

Regression in SRSF space for phase-invariant prediction.

Scalar-on-Shape

Predict a scalar from curve shape via elastic distances and shape PCs.

Cross-Validation

Honest out-of-fold model comparison and component selection.

Regression Diagnostics

Leverage, influence, and residual analysis for functional models.

Uncertainty Quantification

Bootstrap confidence bands and prediction intervals.

Explainability

SHAP, PDP, permutation importance, and significant regions.

Conformal Prediction

Distribution-free prediction intervals with split conformal.

Conformal Classification

Prediction sets with finite-sample coverage guarantees.

Robust Regression

Depth-weighted and trimmed regression resistant to outliers.