SRAE: evidence-screened empirical-Bayes additive models

SRAE fits an interpretable order-two functional-ANOVA model

\[f(\mathbf{x}) \;=\; \beta_0 \;+\; \sum_{j} f_j(x_j) \;+\; \sum_{(j,k)\,\in\,\mathcal{S}} f_{jk}(x_j, x_k)\]

with penalized-spline main effects and a small set of automatically screened pairwise tensor interactions. The roughness precisions \(\lambda_j\), the null-space precisions \(\kappa_j\), and (for Gaussian regression) the residual variance \(\sigma^2\) are estimated from a marginal-likelihood objective rather than by cross-validated grid search.

Every fitted component is a plottable one- or two-dimensional function with a pointwise credible band, and model capacity is reported as effective degrees of freedom per component.

Note

Basis resolution, candidate-pair caps, screening thresholds, and maximum interaction counts remain structural settings chosen by the user. Only the continuous shrinkage parameters are estimated internally. See Scope and limitations.

Getting started

• Installation
  • Requirements
  • From source
  • Optional extras
  • Building the documentation
  • Verifying the installation
• Quick start
  • Regression
  • Classification
  • Inspecting components
  • Using pandas
  • scikit-learn integration
  • Choosing a variant

User guide

• User guide
  • 1. The model
  • 2. Inference
  • 3. Interaction discovery
  • 4. Estimator variants
  • 5. Interpreting a fitted model
  • Notation

Reference

• API reference
  • Regression estimators
  • Classification estimators
  • Plotting
  • Inference engines
  • Basis blocks
• Glossary

Estimator overview

Eight estimators span a \(2 \times 2\) design over two independent axes, crossed with the regression / classification task.

Regularization	Hyperprior	Regression	Classification
Type-II MLE	point estimate	SRAERegressor	SRAEClassifier
pooled stack	point estimate	SRAERegressorPooled	SRAEClassifierPooled
Type-II MLE	integrated	SRAERegressorSI	SRAEClassifierSI
pooled stack	integrated	SRAERegressorSIPooled	SRAEClassifierSIPooled

The regularization axis selects how the block hyperparameters \((\lambda_j, \kappa_j)\) are estimated; the hyperprior axis selects whether those hyperparameters are used as a point estimate or integrated over. See Estimator variants for when each is appropriate.

Scope and limitations

• The model is restricted to smooth main effects and selected pairwise interactions; no three-way or higher terms.

• Interaction discovery is greedy and conditional on the main-effect fit. The screening score is a conditional residual marginal likelihood, not an exact Bayes factor for the full model — especially under the logistic likelihood.

• The product-correlation pre-ranking used when the candidate set exceeds max_screen_pairs can miss interactions that are symmetric, masked, or poorly represented by a centered product.

• Uncertainty summaries condition on the estimated hyperparameters, the selected interaction set, and the fixed basis. They do not propagate interaction-selection uncertainty.

• Multiclass classification is one-vs-rest, not a jointly estimated multinomial model; the row-normalized probabilities are not guaranteed calibrated.

• The logistic path is approximate (Laplace); evidence monotonicity is not guaranteed by the Gaussian EM argument.

• The implementation uses dense linear algebra and does not accept sparse input, missing values, or non-numeric columns.

Indices

• Index

• Module Index

• Search Page