sgl_fit: Fit a sparse group lasso regularization path.
In sglOptim: Sparse group lasso generic optimizer

Description Usage Arguments Value Author(s)

A sequence of minimizers (one for each lambda given in the lambda argument) of

\mathrm{loss}(β) + λ ≤ft( (1-α) ∑_{J=1}^m γ_J \|β^{(J)}\|_2 + α ∑_{i=1}^{n} ξ_i |β_i| \right)

where \mathrm{loss} is the loss/objective function specified by module_name. The parameters are organized in the parameter matrix β with dimension q\times p. The vector β^{(J)} denotes the J parameter group. The group weights γ \in [0,∞)^m and the parameter weights ξ = (ξ^{(1)},…, ξ^{(m)}) \in [0,∞)^n with ξ^{(1)}\in [0,∞)^{n_1},…, ξ^{(m)} \in [0,∞)^{n_m}.

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sgl_fit(module_name, PACKAGE, data, parameterGrouping, groupWeights,
  parameterWeights, alpha, lambda, return = 1:length(lambda),
  algorithm.config = sgl.standard.config)

`module_name`	reference to objective specific C++ routines.
`PACKAGE`	name of the calling package.
`data`	a list of data objects – will be parsed to the specified module.
`parameterGrouping`	grouping of parameters, a vector of length p. Each element of the vector specifying the group of the parameters in the corresponding column of β.
`groupWeights`	the group weights, a vector of length `length(unique(parameterGrouping))` (the number of groups).
`parameterWeights`	a matrix of size q \times p.
`alpha`	the α value 0 for group lasso, 1 for lasso, between 0 and 1 gives a sparse group lasso penalty.
`lambda`	the lambda sequence for the regularization path.
`return`	the indices of lambda values for which to return fitted parameters.
`algorithm.config`	the algorithm configuration to be used.

`beta`	the fitted parameters – a list of length `length(return)` with each entry a matrix of size q\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.