jade_admm: Fit JADE
In jean997/jadeTF:

This is the main function in the jadeTF package. It fits JADE by minimizing

∑_i=1^K ( n_i/2 || A_i y_i - θ_i ||_2^2 + λ_i || D θ_i||_1) + γ ∑_{j < l}|| W_jl (θ_j - θ_l) ||_1

jade_admm(y, gamma, pos = NULL, lambda = NULL, sample.size = NULL,
  ord = 2, sds = NULL, fit.var = NULL, var.wts = NULL,
  subset.wts = NULL, theta0 = NULL, u.alpha0 = NULL, u.beta0 = NULL,
  verbose = FALSE, tol = 0.001, max.it = 1000, cv.metric = c("mse",
  "abs", "pois"), rho.alpha = NULL, rho.beta = 1, adjust.rho.alpha = TRUE,
  fix.rho.after = 500, tau.decr = 2, tau.incr = 2, mu = 10,
  e.rel = 1e-04, e.abs = 1e-08)

`y`	Data matrix of size p x K. May contain NA values but may not contain rows which are all NA.
`gamma`	Fusion penalty.
`pos`	Position vector of length p. If missing will use 1:p.
`lambda`	Smoothing penalty vecor of length K. If not provided, lambda will be chosen by cross validation.
`sample.size`	Vector of sample sizes of length K. If missing sample sizes are assumed to be 1.
`ord`	Order of polynomial to fit. May be 0, 1, or 2.
`sds`	Matrix of estimated standard deviations of size p x K. These are the inverse of the diagonal elements of A_i. Only the relative sizes of `sds` is important.
`fit.var`	Matrix of size p x K of estimated variance of trendfiltering fits. This will be used to construct the pairwise weight matrices W. Currently this is only supported for K=2. `fit.var` can be estimated by bootstrapping. See `bs_var_tf`.
`var.wts`	If `fit.var` is not provided, the diagonal elements of W may be specified here. Since pairwise weights are currently only allowed for K=2, `var.wts` must be a vector of length p.
`subset.wts`	This option can be used to obtain a de-biased fit with the γ penalty only applied to pairs of points previously determined to be fused. It should be a list of lists of the same format as the output of `get_sep`. Elements are vectors of length p of 0s and 1s with 0 indicating that the pair of points should not be penalized.
`theta0,u.alpha0,u.beta0`	Starting values for θ and the dual variables. If a solution has been found for a nearby value of γ using these values can improve convergence time. If not provided the solution at γ = 0 is used.
`verbose`	Be chattier.
`tol`	Tolerance for declaring points separated. Separation can be recalculated with a different value of `tol` using `get_sep`.
`max.it`	Maximum number of iterations.
`cv.metric`	Metric to use for selection of lambda - can be "mse"(mean squared error), "abs"(absolute value), or "pois"(Poisson).
`rho.alpha,rho.beta`	ADMM step sizes. `rho.alpha` has length K and `rho.beta` is a constant. Change with caution.
`adjust.rho.alpha`	Adaptively change rho.alpha. This does not seem to help so the default is FALSE.
`tau.incr,tau.decr,mu`	Parameters for adjusting step size. Change with caution.
`e.rel,e.abs`	Parameters for determining convergence. Change with caution.