cglasso: Fits regularization paths for group-lasso penalized learning...
In Zhe-Research/compReg: Compositional Data Regression

Description Usage Arguments Value

Fits regularization paths for linear constraints group-lasso penalized learning problems at a sequence of regularization parameters lambda.

cglasso(y, Z, Zc = NULL, k, W = rep(1, times = p), intercept = TRUE,
  A = kronecker(matrix(1, ncol = p), diag(k)), b = rep(0, times = k),
  u = 1, mu_ratio = 1.01, lam = NULL, nlam = 100,
  lambda.factor = ifelse(n < p1, 0.05, 0.001), dfmax = p,
  pfmax = min(dfmax * 1.5, p), tol = 0, outer_maxiter = 3e+08,
  outer_eps = 1e-08, inner_maxiter = 1e+06, inner_eps = 1e-08)

`y`	a vector of response variable with length n.
`Z`	a matrix, of dimension np1*, for predictors to be imposed with group lasso penalty.
`Zc`	a design matrix for those group-lasso-penalty free predictors. Can be missing. Default value is NULL.
`k`	k is the size for each group in Z. All groups are with the same size. Number of groups is p = p1 / k .
`W`	a vector in length of p (the total number of groups), matrix with dimension `p1*p1` or character specifying function used to caculate weight matrix for each group. If vector, works as penalty factor. Separate penalty weights can be applied to each group of beta'ss to allow differential shrinkage. Can be 0 for some groups, which implies no shrinkage, and results in that group always being included in the model. If matrix, a block diagonal matrix. Diagonal elements are inverted weights matrics for each group. if character, user should provide the function. Default value is rep(1, times = p).
`intercept`	whether to include intercept. Default is TRUE.
`A, b`	linear equality constraints Aβ_p1 = b, where b is a vector with length k, and A is a kp1* matrix. Default values, b is a vector of 0's and `A = kronecker(matrix(1, ncol = p), diag(k))`.
`u`	`u` is the inital value for penalty parameter of augmented Lanrange method adopted in outer loop - default value is 1.
`mu_ratio`	`mu_ratio` is the increasing ratio for `u` - default value is 1.01. Inital values for scaled Lagrange multipliers are set as 0's. If `mu_ratio` < 1, there is no linear constraints included. Group lasso coefficients are estimated.
`lam`	a user supplied lambda sequence. Typically, by leaving this option unspecified users can have the program compute its own `lam` sequence based on `nlam` and `lambda.factor` If `lam` is provided but a scaler, `lam` sequence is also created starting from `lam`. Supplying a value of lambda overrides this. It is better to supply a decreasing sequence of lambda values, if not, the program will sort user-defined `lambda` sequence in decreasing order automatically.
`nlam`	the length of `lam` sequence - default is 100.
`lambda.factor`	the factor for getting the minimal lambda in `lam` sequence, where `min(lam)` = `lambda.factor` * `max(lam)`. `max(lam)` is the smallest value of `lam` for which all penalized group are zero's. The default depends on the relationship between n and p1 If n >= p1 the default is `0.001`, close to zero. If n < p1, the default is `0.05`. A very small value of `lambda.factor` will lead to a saturated fit. It takes no effect if there is user-defined lambda sequence.
`dfmax`	limit the maximum number of groups in the model. Useful for very large p, if a partial path is desired - default is p.
`pfmax`	limit the maximum number of groups ever to be nonzero. For example once a group enters the model along the path, no matter how many times it exits or re-enters model through the path, it will be counted only once. Default is `min(dfmax*1.5, p)`.
`tol`	tolerance for vectors beta'ss to be considered as none zero's. For example, coefficient β_j for group j, if max(abs(β_j)) < `tol`, set β_j as 0's. Default value is 0.
`outer_maxiter, outer_eps`	`outer_maxiter` is the maximun munber of loops allowed for Augmented Lanrange method; and `outer_eps` is the convergence termination tolerance.
`inner_maxiter, inner_eps`	`inner_maxiter` is the maximun munber of loops allowed for blockwise-GMD; and `inner_eps` is the convergence termination tolerance.

A list

`lam`	the actual sequence of lambda values used
`df`	the number of nonzero groups in estimated coefficients for `Z` at each value of lambda
`path`	a matrix of coefficients