msgl (version 0.1.3)

msgl: Fit a multinomial sparse group lasso regularization path.

Description

For a classification problem with $K$ classes and $p$ covariates dived into $m$ groups. A sequence of minimizers (one for each lambda given in the lambda argument) of $$\hat R(\beta) + \lambda \left( (1-\alpha) \sum_{J=1}^m \gamma_J \|\beta^{(J)}\|_2 + \alpha \sum_{i=1}^{n} \xi_i |\beta_i| \right)$$ where $\hat R$ is the weighted empirical log-likelihood risk of the multinomial regression model. The vector $\beta^{(J)}$ denotes the parameters associated with the $J$'th group of covariates (default is one covariate per group, hence the default dimension of $\beta^{(J)}$ is $K$). The group weights $\gamma \in [0,\infty)^m$ and the parameter weights $\xi = (\xi^{(1)},\dots, \xi^{(m)}) \in [0,\infty)^n$ with $\xi^{(1)}\in [0,\infty)^{n_1},\dots, \xi^{(m)} \in [0,\infty)^{n_m}$.

Usage

msgl(x, classes,
    sampleWeights = rep(1/length(classes), length(classes)),
    grouping = NULL, groupWeights = NULL,
    parameterWeights = NULL, alpha = 0.5,
    standardize = TRUE, lambda, return = 1:length(lambda),
    sparse.data = FALSE,
    algorithm.config = sgl.standard.config)

Arguments

x

design matrix, matrix of size $N \times p$.

classes

classes, factor of length $N$.

sampleWeights

sample weights, a vector of length $N$.

grouping

grouping of covariates, a vector of length $p$. Each element of the vector specifying the group of the covariate.

groupWeights

the group weights, a vector of length $m+1$ (the number of groups). The first element of the vector is the intercept weight. If groupWeights = NULL default weights will be used. Default weights are 0 for the intercept and $$\sqrt{K\cd

parameterWeights

a matrix of size $K \times (p+1)$. The first column of the matrix is the intercept weights. Default weights are is 0 for the intercept weights and 1 for all other weights.

alpha

the $\alpha$ value 0 for group lasso, 1 for lasso, between 0 and 1 gives a sparse group lasso penalty.

standardize

if TRUE the covariates are standardize before fitting the model. The model parameters are returned in the original scale.

lambda

the lambda sequence for the regularization path.

return

the indices of lambda values for which to return a the fitted parameters.

sparse.data

if TRUE x will be treated as sparse, if x is a sparse matrix it will be treated as sparse by default.

algorithm.config

the algorithm configuration to be used.

Value

• beta
  the fitted parameters -- a list of length length(lambda) with each entry a matrix of size $K\times (p+1)$ holding the fitted parameters
• loss
  the values of the loss function
• objective
  the values of the objective function (i.e. loss + penalty)
• lambda
  the lambda values used

Examples

data(SimData)
x <- sim.data$x
classes <- sim.data$classes
lambda <- msgl.lambda.seq(x, classes, alpha = .5, d = 100L, lambda.min = 0.01)
fit <- msgl(x, classes, alpha = .5, lambda = lambda)
fit$beta[[10]] #model with lambda = lambda[10]