samQL: Training function of Sparse Additive Regression with...

In SAM: Sparse Additive Modelling

Training function of Sparse Additive Regression with Quadratic Loss

Description

Fit a sparse additive regression model with quadratic loss.

Usage

samQL(
  X,
  y,
  p = 3,
  lambda = NULL,
  nlambda = NULL,
  lambda.min.ratio = 0.005,
  thol = 1e-05,
  max.ite = 1e+05,
  regfunc = "L1"
)

Arguments

X	Numeric training matrix with n rows (samples) and d columns (features).
y	Numeric response vector of length n.
p	The number of basis spline functions. The default value is 3.
lambda	Optional user-supplied regularization sequence. If provided, use a decreasing sequence; warm starts are used along the path and are usually much faster than fitting a single value.
nlambda	The number of lambda values. The default value is 30.
lambda.min.ratio	Smallest lambda as a fraction of lambda.max (the smallest value that keeps all component functions at zero). The default is 5e-3.
thol	Stopping tolerance. The default value is 1e-5.
max.ite	Maximum number of iterations. The default value is 1e5.
regfunc	A string indicating the regularizer. The default value is "L1". You can also assign "MCP" or "SCAD" to it.

Details

The solver combines block coordinate descent, fast iterative soft-thresholding, and Newton updates. Computation is accelerated by warm starts and active-set screening.

Value

p	The number of basis spline functions used in training.
X.min	Per-feature minimums from training data (used to rescale test data).
X.ran	Per-feature ranges from training data (used to rescale test data).
lambda	Sequence of regularization parameters used in training.
w	Solution path matrix with size d*p by length(lambda); each column corresponds to one regularization parameter.
intercept	The solution path of the intercept.
df	Degrees of freedom along the solution path (number of non-zero component functions).
knots	The p-1 by d matrix. Each column contains the knots applied to the corresponding variable.
Boundary.knots	The 2 by d matrix. Each column contains the boundary points applied to the corresponding variable.
func_norm	Functional norm matrix (d by length(lambda)); each column corresponds to one regularization parameter.
sse	Sums of square errors of the solution path.

See Also

SAM,plot.samQL,print.samQL,predict.samQL

Examples

## generating training data
n = 100
d = 500
X = 0.5*matrix(runif(n*d),n,d) + matrix(rep(0.5*runif(n),d),n,d)

## generating response
y = -2*sin(X[,1]) + X[,2]^2-1/3 + X[,3]-1/2 + exp(-X[,4])+exp(-1)-1

## Training
out.trn = samQL(X,y)
out.trn

## plotting solution path
plot(out.trn)

## generating testing data
nt = 1000
Xt = 0.5*matrix(runif(nt*d),nt,d) + matrix(rep(0.5*runif(nt),d),nt,d)

yt = -2*sin(Xt[,1]) + Xt[,2]^2-1/3 + Xt[,3]-1/2 + exp(-Xt[,4])+exp(-1)-1

## predicting response
out.tst = predict(out.trn,Xt)

SAM documentation built on Feb. 19, 2026, 5:06 p.m.