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Fit a graphical lasso over a path of penalties

Source: R/glasso.R
glasso_path.Rd

Runs glasso_fit() at every penalty in rho, warm-starting each fit from the previous one. This is the kernel behind bootstrap and resampling workflows that need many refits of the same covariance.

Usage

glasso_path(
  S,
  rho,
  penalize_diagonal = FALSE,
  max_outer = 10000,
  tol_outer = 1e-04,
  max_inner = 10000,
  tol_inner = 1e-04
)

Arguments

S

Covariance or correlation matrix (p x p, symmetric, finite).

rho

Numeric vector of non-negative penalties, used in the order supplied.

penalize_diagonal

Logical. Penalise the diagonal of Theta as well? Default FALSE, matching the usual EBIC-glasso convention.

max_outer, max_inner

Outer (column-sweep) and inner (coordinate-descent) iteration caps, as in glasso_fit().

tol_outer, tol_inner

Convergence tolerances. The defaults are the looser path tolerances (1e-4), matching glasso::glassopath(): path scanning selects among well-separated models, so machine precision at every rung buys nothing. Refit the selected penalty with glasso_fit() when the returned matrix itself must be at full precision.

Value

An object of class glasso_path_result: a list with w and wi, each a p x p x length(rho) array indexed in the order rho was supplied, plus the rho vector itself. Use as.data.frame() for a tidy one-row-per-edge-per-penalty table.

See also

glasso_fit()

Examples

set.seed(1)
z <- rnorm(200)
x <- cbind(A = z + rnorm(200, 0, 0.5), B = z + rnorm(200, 0, 0.5),
           C = rnorm(200), D = rnorm(200))
path <- glasso_path(cov(x), rho = c(0.01, 0.05, 0.2))
path
#> Graphical Lasso Path
#>   Variables:      4
#>   Penalties:      3 (0.01 to 0.2)
#>   Nonzero edges:  4, 3, 1
#> 
#>   as.data.frame(x)
as.data.frame(path)
#>     rho from to   precision      weight
#> 1  0.01    A  B -1.49912964 0.751703867
#> 2  0.01    A  C -0.04203394 0.031587449
#> 3  0.01    C  D -0.02373780 0.027607344
#> 4  0.01    A  D -0.03528085 0.025989049
#> 5  0.01    B  C  0.00000000 0.000000000
#> 6  0.01    B  D  0.00000000 0.000000000
#> 7  0.05    A  B -1.28019986 0.717722626
#> 8  0.05    A  C -0.01229880 0.009791150
#> 9  0.05    A  D -0.00454654 0.003547031
#> 10 0.05    B  C  0.00000000 0.000000000
#> 11 0.05    B  D  0.00000000 0.000000000
#> 12 0.05    C  D  0.00000000 0.000000000
#> 13 0.20    A  B -0.77729717 0.588053200
#> 14 0.20    A  C  0.00000000 0.000000000
#> 15 0.20    B  C  0.00000000 0.000000000
#> 16 0.20    A  D  0.00000000 0.000000000
#> 17 0.20    B  D  0.00000000 0.000000000
#> 18 0.20    C  D  0.00000000 0.000000000