tune_Lambda: Tune Smoothing and Ridge Penalties via Generalized Cross...

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Tune Smoothing and Ridge Penalties via Generalized Cross Validation

Description

Optimizes smoothing spline and ridge regression penalties by minimizing GCV criterion. Uses BFGS optimization with analytical gradients or finite differences.

Usage

tune_Lambda(
  y,
  X,
  X_gram,
  smoothing_spline_penalty,
  A,
  K,
  nc,
  nr,
  opt,
  use_custom_bfgs,
  C,
  colnm_expansions,
  wiggle_penalty,
  flat_ridge_penalty,
  invsoftplus_initial_wiggle,
  invsoftplus_initial_flat,
  unique_penalty_per_predictor,
  unique_penalty_per_partition,
  invsoftplus_penalty_vec,
  meta_penalty,
  family,
  unconstrained_fit_fxn,
  keep_weighted_Lambda,
  iterate,
  qp_score_function,
  quadprog,
  qp_Amat,
  qp_bvec,
  qp_meq,
  tol,
  sd_y,
  delta,
  constraint_value_vectors,
  parallel,
  parallel_eigen,
  parallel_trace,
  parallel_aga,
  parallel_matmult,
  parallel_unconstrained,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks,
  shared_env,
  custom_penalty_mat,
  order_list,
  glm_weight_function,
  shur_correction_function,
  need_dispersion_for_estimation,
  dispersion_function,
  observation_weights,
  homogenous_weights,
  blockfit,
  just_linear_without_interactions,
  Vhalf,
  VhalfInv,
  verbose,
  include_warnings,
  ...
)

Arguments

y	List; response vectors by partition
X	List; design matrices by partition
X_gram	List; Gram matrices by partition
smoothing_spline_penalty	Matrix; integrated squared second derivative penalty
A	Matrix; smoothness constraints at knots
K	Integer; number of interior knots in 1-D, number of partitions - 1 in higher dimensions
nc	Integer; columns per partition
nr	Integer; total sample size
opt	Logical; TRUE to optimize penalties, FALSE to use initial values
use_custom_bfgs	Logical; TRUE for analytic gradient BFGS as natively implemented, FALSE for finite differences as implemented by stats::optim().
wiggle_penalty, flat_ridge_penalty	Initial penalty values
invsoftplus_initial_wiggle, invsoftplus_initial_flat	Initial grid search values (log scale)
unique_penalty_per_predictor, unique_penalty_per_partition	Logical; allow predictor/partition-specific penalties
invsoftplus_penalty_vec	Initial values for predictor/partition penalties (log scale)
meta_penalty	The "meta" ridge penalty, a regularization for predictor/partition penalties to pull them on log-scale towards 0 (1 on raw scale)
family	GLM family with optional custom tuning loss
keep_weighted_Lambda, iterate	Logical controlling GLM fitting
qp_score_function, quadprog, qp_Amat, qp_bvec, qp_meq	Quadratic programming parameters (see arguments of lgspline)
tol	Numeric; convergence tolerance
sd_y, delta	Response standardization parameters
constraint_value_vectors	List; constraint values
parallel	Logical; enable parallel computation
cl, chunk_size, num_chunks, rem_chunks	Parallel computation parameters
custom_penalty_mat	Optional custom penalty matrix
order_list	List; observation ordering by partition
glm_weight_function, shur_correction_function	Functions for GLM weights and corrections
need_dispersion_for_estimation, dispersion_function	Control dispersion estimation
observation_weights	Optional observation weights
homogenous_weights	Logical; TRUE if all weights equal
blockfit	Logical; when TRUE, block-fitting (not per-partition fitting) approach is used, analogous to quadratic programming.
just_linear_without_interactions	Numeric; vector of columns of input predictor matrix that correspond to non-spline effects without interactions, used for block-fitting.
Vhalf, VhalfInv	Square root and inverse square root correlation structures for fitting GEEs.
verbose	Logical; print progress
include_warnings	Logical; print warnings/try-errors
...	Additional arguments passed to fitting functions

Details

Uses BFGS optimization to minimize GCV criterion for penalty selection. Supports analytical gradients for efficiency with standard GLM families. Can optimize unique penalties per predictor/partition. Handles custom loss functions and GLM weights. Parallel computation available for large problems.

Value

List containing:

• Lambda - Final combined penalty matrix

• flat_ridge_penalty - Optimized ridge penalty

• wiggle_penalty - Optimized smoothing penalty

• other_penalties - Optimized predictor/partition penalties

• L_predictor_list - Predictor-specific penalty matrices

• L_partition_list - Partition-specific penalty matrices

See Also

• optim for Hessian-free optimization

lgspline documentation built on June 8, 2025, 10:45 a.m.