asgl: Fit a GLM with Adaptive Sparse Group Lasso Penalty

In jeffdaniel/asgl: Fit a GLM with Adaptive Sparse Group Lasso Penalty

Description

Fit a generalized linear model via penalized maximum likelihood. The regularization path is computed for the adaptive sparse group lasso penalty along a sequence of tuning parameter values. Supports linear and logistic regression.

Usage

asgl(x, y, index, family = c("gaussian", "binomial"), offset = NULL,
  alpha = 0.95, lambda = NULL, lambda_min = 0.1, nlambda = 20,
  maxit = 1000, thresh = 0.001, gamma = 0.8, step = 1,
  standardize = FALSE, grp_weights = NULL, ind_weights = NULL)

Arguments

x	Input matrix of dimensions n by p.
y	Response vector of length n. For linear models (family = "gaussian"), a numeric vector; for logistic models (family = "binomial"), a categorical factor with two levels.
index	A vector of length p defining group membership for each covariate.
family	Response type. One of "gaussian" or "binomial".
offset	Optional. A vector of length n to be included in the linear predictor
alpha	Penalty mixing parameter. The penalty reduces to the adaptive group lasso if alpha = 0 and to the adaptive lasso if alpha = 0.
lambda	Optional. A vector of user-specified penalty tuning parameter values at which to fit model. If NULL, the sequence is chosen automatically (recommended).
lambda_min	Smallest tuning parameter value, as a fraction of the largest parameter value in the sequence (the smallest value for which all coefficients are zero).
nlambda	The number of tuning parameter values in the sequence.
maxit	Maximum number of iterations until convergence
thresh	Convergence threshold for change in model coefficient values.
gamma	Backtracking parameter for use in gradient descent step
step	Initial gradient descent step size.
standardize	If TRUE, variables are standardized prior to model fitting.
grp_weights	A vector of weights for each group of coefficients, the same length as index.
ind_weights	A vector of weights for each indiviual coefficient, of length p.

Value

An object of class "asgl"

Examples

# linear regression
n <- 500; p <- 20; groupsize <- 5
index <- ceiling(1:p / groupsize)
beta <- (-2:2)
x <- matrix(rnorm(n * p), ncol = p, nrow = n)
y <- as.vector(x[,1:5] %*% beta + 0.1 * rnorm(n))
asgl(x, y, index, family = "gaussian")

# logistic regression
eta <- x[, 1:5] %*% beta
prob <- exp(eta) / (1 + exp(eta))
y <- rbinom(n, 1, prob)
asgl(x, y, index, family = "binomial")

# adaptive weights
coefs <- glm.fit(x, y, family = binomial())$coefficients
ind_weights <- 1 / abs(coefs)
grp_weights <- numeric(length(unique(index)))
for (i in unique(index)) {
  grp_weights[i] <-  1 / sqrt(sum(coefs[which(index == i)]^2))
}
asgl(x, y, index, family = "binomial",
     grp_weights = grp_weights, ind_weights = ind_weights)

jeffdaniel/asgl documentation built on Nov. 4, 2019, 2:37 p.m.