ggb: ggb: Graph-Guided Banding for Covariance Estimation
In jacobbien/ggb: Graph-Guided Banding of the Covariance Matrix

Description Usage Arguments Details See Also Examples

This package implements the two methods introduced in Bien, J. (2018) "Graph-Guided Banding of the Covariance Matrix." Journal of the American Statistical Association. http://arxiv.org/abs/1606.00451

Computes the global or local GGB estimator (depending on type argument) along a grid of lambda values.

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ggb(S, g, type = c("global", "local"), lambda = NULL, delta = NULL,
  flmin = 0.01, nlam = 20, max_depths = NULL, out_iter = 100,
  in_iter = 500, out_tol = 1e-04, in_tol = 1e-04, verbose = 0)

`S`	p-by-p sample covariance matrix
`g`	seed graph (not necessarily connected)
`type`	either "global" or "local"
`lambda`	positive tuning parameter(s)
`delta`	lower bound on eigenvalues (default, NULL, means no bound)
`flmin`	ratio of smallest to largest lambda value (ignored if `lambda` is nonnull)
`nlam`	number of lambda values (ignored if `lambda` is nonnull)
`max_depths`	maximal bandwidth(s) considered. If type is "global", this must be a single non-negative integer. If type is "local", this must be a p-vector of non-negative integers. Default is NULL, which is equivalent to taking max_depths to be >= diameter(g). (These are referred to as M and M_j in the paper.)
`out_iter`	number of iterations of outer loop (i.e., # of eigenvalue decompositions). Ignored when `delta` is NULL.
`in_iter`	number of iterations on inner loop (i.e., # cycles over row/cols) when `type` is "local".
`out_tol`	convergence threshold for outer loop BCD (ignored when `delta` is NULL)
`in_tol`	convergence threshold for inner loop BCD when `type` is "local".
`verbose`	level of verbosity in printed output (3, 2, 1, 0)

The main function is ggb.

To evaluate the proximal operator, it uses the "closed form" of Yan and Bien (2015) for the global GGB estimator as implemented in the R package hsm and uses blockwise coordinate descent for the local GGB estimator.

If delta is non-NULL, then alternates between evaluating proximal operator and projecting eigenvalues.

The weights used in this penalty are the square root of the group size.

cv_ggb

set.seed(123)
n <- 100
p <- 20
g <- igraph::graph.lattice(c(5, 4))
x <- matrix(rnorm(n * p), n, p)
S <- cov(x)
fit_global <- ggb(S, g, type = "global", nlam = 10)
fit_local <- ggb(S, g, type = "local", nlam = 10)