Adaptive Regional Functional Regression with AdaReFun • AdaReFun

Model family

AdaReFun is short for Adaptive Regional Functional Regression. It fits scalar-on-function regression with a common B-spline coefficient vector and folded-concave regional penalties. ARFC denotes the adaptive regional folded-concave estimator family. The public interface contains four adaptive regional candidates:

Resolution	MCP	SCAD
Single	ASR-MCP	ASR-SCAD
Multi	AMR-MCP	AMR-SCAD

The established fixed-resolution fMCP() and fSCAD() estimators are also retained as comparators; they are not automatic candidates in ARFC-Select.

Direct fitting of one ARFC specification

The user supplies both tuning grids. The smooth-pilot BIC selects one roughness value, after which the regional path is evaluated on the common lambda grid.

library(AdaReFun)

fit <- arfc(
  y, x, argvals,
  lambda = 10^seq(-5, -1, length.out = 10),
  kappa = 10^seq(-7, -2, length.out = 6),
  resolution = "multi",
  penalty = "MCP",
  levels = c(8L, 16L, 32L)
)

summary(fit)
plot(fit, type = "coefficient")
plot(fit, type = "regions")
plot(fit, type = "weights")
plot(fit, type = "tuning")

Selecting among four candidates

arfc_select() fits all four candidates on the training sample and returns the one with the lowest MSE on the supplied validation sample.

selected <- arfc_select(
  y_train, x_train, argvals,
  validation = list(y = y_validation, x = x_validation),
  lambda = 10^seq(-5, -1, length.out = 10),
  kappa = 10^seq(-7, -2, length.out = 6),
  levels = c(8L, 16L, 32L)
)

selected$selection
plot(selected, type = "validation")
plot(selected, type = "candidates")

Numerical details

Exact zeros arise from coefficient thresholding followed by an active-set roughness refit. The full tuning table retains failed, nonconverged, and objective-increase diagnostics. MCP and SCAD are nonconvex, so the fitted solutions are local solutions associated with the documented smooth-pilot initialization.

With the default shapes, MCP gamma = 2.7 and SCAD a = 3.7 have equal scalar maximum concavity. This calibration does not by itself imply that two complete overlapping multi-resolution objectives have identical global curvature.

Citation

AdaReFun is developed by Bahadır Yüzbaşı and Jiguo Cao. The package citation is returned by:

citation("AdaReFun")

Package source and replication materials are available at byuzbasi/AdaReFun.