islasso.path: Induced Smoothed Lasso Regularization Path

In islasso: The Induced Smoothed Lasso

Induced Smoothed Lasso Regularization Path

Description

Fits a sequence of penalized regression models using the Induced Smoothing Lasso approach over a grid of lambda values. Supports elastic-net penalties and generalized linear models: Gaussian, Binomial, Poisson, and Gamma.

Usage

islasso.path(
  formula,
  family = gaussian(),
  lambda = NULL,
  nlambda = 100,
  lambda.min.ratio = ifelse(nobs < nvars, 0.01, 1e-04),
  alpha = 1,
  data,
  weights,
  subset,
  offset,
  contrasts = NULL,
  unpenalized,
  control = is.control()
)

Arguments

formula	Model formula of type response ~ predictors.
family	Response distribution. Supported families: gaussian(), binomial(), poisson(), Gamma().
lambda	Optional numeric vector of lambda values. If not provided, a sequence is automatically generated.
nlambda	Integer. Number of lambda values to generate if lambda is missing. Default is 100.
lambda.min.ratio	Smallest lambda as a fraction of lambda.max. Default: 1e-2 if nobs < nvars, else 1e-3.
alpha	Elastic-net mixing parameter: alpha = 1 is lasso, alpha = 0 is ridge.
data	Data frame containing model variables.
weights	Optional observation weights.
subset	Optional logical or numeric vector to subset observations.
offset	Optional vector of prior known components for the linear predictor.
contrasts	Optional contrast settings for factor variables.
unpenalized	Optional vector of variable names or indices excluded from penalization.
control	A list of control parameters via is.control.

Details

This function fits a regularization path of models using the induced smoothing paradigm, replacing the non-smooth L1 penalty with a differentiable surrogate. Standard errors are returned for all lambda points, allowing for Wald-based hypothesis testing. The regularization path spans a range of lambda values, either user-defined or automatically computed.

Value

A list with components:

call	Matched function call.
Info	Matrix with diagnostics: lambda, deviance, degrees of freedom, dispersion, iterations, convergence status.
GoF	Model goodness-of-fit metrics: AIC, BIC, AICc, GCV, GIC, eBIC.
Coef	Matrix of coefficients across lambda values.
SE	Matrix of standard errors.
Weights	Matrix of mixing weights for the smoothed penalty.
Gradient	Matrix of gradients for the smoothed penalty.
Linear.predictors, Fitted.values, Residuals	Matrices of fitted quantities across the path.
Input	List of input arguments and design matrix.
control, formula, model, terms, data, xlevels, contrasts	Standard model components.

Author(s)

Gianluca Sottile [e-mail]

References

Cilluffo G., Sottile G., La Grutta S., Muggeo V.M.R. (2019). The Induced Smoothed Lasso: A practical framework for hypothesis testing in high dimensional regression. Statistical Methods in Medical Research. DOI: 10.1177/0962280219842890

Sottile G., Cilluffo G., Muggeo V.M.R. (2019). The R package islasso: estimation and hypothesis testing in lasso regression. Technical Report. DOI: 10.13140/RG.2.2.16360.11521

See Also

islasso, summary.islasso.path, coef.islasso.path, predict.islasso.path, GoF.islasso.path

Examples

n <- 100; p <- 30; p1 <- 10  # number of nonzero coefficients

beta.veri <- sort(round(c(seq(.5, 3, length.out = p1/2),
                         seq(-1, -2, length.out = p1/2)), 2))
beta <- c(beta.veri, rep(0, p - p1))
sim1 <- simulXy(n = n, p = p, beta = beta, seed = 1, family = gaussian())
o <- islasso.path(y ~ ., data = sim1$data,
                  family = gaussian(), nlambda = 30L)
o

summary(o, lambda = 10, pval = 0.05)
coef(o, lambda = 10)
fitted(o, lambda = 10)
predict(o, type = "response", lambda = 10)
plot(o, yvar = "coef")
residuals(o, lambda = 10)
deviance(o, lambda = 10)
logLik(o, lambda = 10)
GoF.islasso.path(o)

## Not run: 
##### binomial ######
beta <- c(1, 1, 1, rep(0, p - 3))
sim2 <- simulXy(n = n, p = p, beta = beta, interc = 1, seed = 1,
                size = 100, family = binomial())
o2 <- islasso.path(cbind(y.success, y.failure) ~ ., data = sim2$data,
                   family = binomial(), lambda = seq(0.1, 100, l = 50L))
temp <- GoF.islasso.path(o2)
summary(o2, pval = 0.05, lambda = temp$lambda.min["BIC"])

##### poisson ######
beta <- c(1, 1, 1, rep(0, p - 3))
sim3 <- simulXy(n = n, p = p, beta = beta, interc = 1, seed = 1,
                family = poisson())
o3 <- islasso.path(y ~ ., data = sim3$data, family = poisson(), nlambda = 30L)
temp <- GoF.islasso.path(o3)
summary(o3, pval = 0.05, lambda = temp$lambda.min["BIC"])

##### Gamma ######
beta <- c(1, 1, 1, rep(0, p - 3))
sim4 <- simulXy(n = n, p = p, beta = beta, interc = -1, seed = 1,
                family = Gamma(link = "log"))
o4 <- islasso.path(y ~ ., data = sim4$data, family = Gamma(link = "log"),
                   nlambda = 30L)
temp <- GoF.islasso.path(o4)
summary(o4, pval = .05, lambda = temp$lambda.min["BIC"])

## End(Not run)

islasso documentation built on Aug. 9, 2025, 1:06 a.m.