dot-bf_case_gauss_no_corr: Gaussian Identity Backfitting Without Correlation (Case b)

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Gaussian Identity Backfitting Without Correlation (Case b)

Description

Standard block-coordinate descent on the convex quadratic objective, alternating between the spline step (Lagrangian projection) and the flat step (pooled penalized regression).

Usage

.bf_case_gauss_no_corr(
  X_spline,
  X_flat,
  y,
  K,
  Ghalf_sp,
  GhalfA_sp,
  XfXf_pen_inv,
  constraint_values_spline,
  nc_spline,
  nc_flat,
  A_spline,
  tol,
  max_backfit_iter,
  parallel_qr = FALSE,
  cl = NULL,
  verbose,
  split = NULL,
  constraint_values = list(),
  Lambda_flat = NULL,
  p_expansions = NULL
)

Arguments

X_spline, X_flat	Lists of per-partition submatrices.
y	List of response vectors.
K	Integer.
Ghalf_sp	List of \mathbf{G}_s^{1/2} matrices.
GhalfA_sp	Pre-computed \mathbf{G}_s^{1/2} \mathbf{A}_s.
XfXf_pen_inv	Penalised inverse of the pooled flat Gram matrix.
constraint_values_spline	Spline-only constraint RHS.
nc_spline, nc_flat	Integers.
A_spline	Spline-only constraint matrix.
tol	Convergence tolerance.
max_backfit_iter	Maximum iterations.
verbose	Logical.
split	Output of .bf_split_components, needed for mixed-constraint enforcement on the flat step.
constraint_values	Full constraint RHS list.
Lambda_flat	Flat penalty submatrix.
p_expansions	Integer; columns per partition.

Value

A named list with beta_spline and beta_flat.

lgspline documentation built on Aug. 5, 2026, 1:10 a.m.