Determine support of multiple partial correlation/precision matrices

A simple wrapper for sparsify which determines the support of a list of partial correlation/precision matrix by various methods and returns the sparsified matrices.

sparsify.fused(Plist, ...)

Arguments

Plist

A list of numeric precision matrices.

...

Arguments passed to sparsify.

Value

A list of the same length as Plist with the output from sparsify.

See also

sparsify

Author

Anders Ellern Bilgrau, Wessel N. van Wierigen, Carel F.W. Peeters <carel.peeters@wur.nl>

Examples

ns <- c(10, 11)
Ylist <- createS(ns, p = 16, dataset = TRUE)
Slist <- lapply(Ylist, covML)
Tlist <- default.target.fused(Slist, ns)

# Obtain regularized precision under optimal penalty
opt <- optPenalty.fused.auto(Ylist, Tlist, cv.method = "aLOOCV",
                            maxit.ridgeP.fused = 1500)
#> Found 2 unique penalties of which 0 are interpreted as fixed and 2 are to be determined by aLOOCV.
#> Non-fixed parameters: ridge, fusion
#> Fixed parameters: <none>
#>   Nelder-Mead direct search function minimizer
#> function value for initial parameters = 107.713011
#>   Scaled convergence tolerance is 1.60505e-06
#> Stepsize computed as 4.000000
#> BUILD              3 328.526352 107.713011
#> HI-REDUCTION       5 107.713011 107.189184
#> LO-REDUCTION       7 107.713011 93.010685
#> HI-REDUCTION       9 107.189184 90.102496
#> LO-REDUCTION      11 93.010685 90.102496
#> HI-REDUCTION      13 90.797091 89.739658
#> LO-REDUCTION      15 90.102496 89.660251
#> HI-REDUCTION      17 89.739658 89.587440
#> LO-REDUCTION      19 89.660251 89.565161
#> HI-REDUCTION      21 89.587440 89.561182
#> LO-REDUCTION      23 89.565161 89.559246
#> HI-REDUCTION      25 89.561182 89.553403
#> LO-REDUCTION      27 89.559246 89.553246
#> HI-REDUCTION      29 89.554559 89.553246
#> HI-REDUCTION      31 89.553484 89.553246
#> HI-REDUCTION      33 89.553403 89.553246
#> HI-REDUCTION      35 89.553264 89.553246
#> HI-REDUCTION      37 89.553250 89.553239
#> HI-REDUCTION      39 89.553246 89.553232
#> LO-REDUCTION      41 89.553239 89.553232
#> Exiting from Nelder Mead minimizer
#>     43 function evaluations used
# Use the optimal penalties
Plist <- ridgeP.fused(Slist, ns, lambda = opt$lambda, maxit = 1000)
#> i = 1   | max diff = 2.1757506777e-01
#> i = 2   | max diff = 9.5598204555e-30
#> Converged in 2 iterations, max diff < 1.49e-08.

# Determine support regularized (standardized) precision under optimal penalty
res <- sparsify.fused(Plist, threshold = "top", verbose = FALSE)
#> - Retained elements:  10 
#> - Corresponding to 8.33 % of possible edges 
#>  
#> - Retained elements:  10 
#> - Corresponding to 8.33 % of possible edges 
#>  
round(res[[1]]$sparsePrecision, 1)
#>     A   B   C   D    E    F    G    H   I    J   K    L    M    N    O   P
#> A 1.4 0.0 0.0 0.0  0.0  0.0  0.0  0.0 0.0  0.0 0.0  0.0  0.0  0.0  0.0 0.0
#> B 0.0 1.6 0.0 0.0  0.0  0.3  0.0  0.4 0.0  0.0 0.0  0.0  0.0  0.0  0.0 0.0
#> C 0.0 0.0 1.8 0.0  0.0  0.0  0.0  0.0 0.0  0.0 0.0  0.0  0.0  0.0  0.0 0.5
#> D 0.0 0.0 0.0 1.9  0.0  0.0  0.0  0.0 0.0  0.0 0.0  0.0  0.0  0.0  0.0 0.0
#> E 0.0 0.0 0.0 0.0  2.0  0.0  0.0  0.0 0.0  0.0 0.0 -0.4  0.0  0.0  0.0 0.0
#> F 0.0 0.3 0.0 0.0  0.0  0.9 -0.3 -0.2 0.0  0.0 0.0  0.0  0.0  0.0  0.0 0.0
#> G 0.0 0.0 0.0 0.0  0.0 -0.3  1.3  0.0 0.0  0.0 0.0  0.0  0.0  0.0  0.0 0.0
#> H 0.0 0.4 0.0 0.0  0.0 -0.2  0.0  1.5 0.0  0.0 0.0  0.0  0.0 -0.4  0.0 0.0
#> I 0.0 0.0 0.0 0.0  0.0  0.0  0.0  0.0 1.7  0.0 0.0  0.0  0.0  0.0  0.0 0.0
#> J 0.0 0.0 0.0 0.0  0.0  0.0  0.0  0.0 0.0  1.7 0.0  0.0  0.0  0.0 -0.4 0.0
#> K 0.0 0.0 0.0 0.0  0.0  0.0  0.0  0.0 0.0  0.0 1.8  0.0  0.0  0.0  0.0 0.0
#> L 0.0 0.0 0.0 0.0 -0.4  0.0  0.0  0.0 0.0  0.0 0.0  1.6 -0.3  0.0  0.0 0.0
#> M 0.0 0.0 0.0 0.0  0.0  0.0  0.0  0.0 0.0  0.0 0.0 -0.3  1.5  0.0  0.0 0.3
#> N 0.0 0.0 0.0 0.0  0.0  0.0  0.0 -0.4 0.0  0.0 0.0  0.0  0.0  1.5  0.0 0.0
#> O 0.0 0.0 0.0 0.0  0.0  0.0  0.0  0.0 0.0 -0.4 0.0  0.0  0.0  0.0  1.7 0.0
#> P 0.0 0.0 0.5 0.0  0.0  0.0  0.0  0.0 0.0  0.0 0.0  0.0  0.3  0.0  0.0 1.4
round(res[[2]]$sparsePrecision, 1)
#>     A    B   C    D    E   F   G   H    I   J    K   L   M   N    O    P
#> A 1.7  0.0 0.0  0.0  0.0 0.0 0.0 0.0  0.0 0.5  0.0 0.0 0.0 0.0  0.0  0.0
#> B 0.0  1.5 0.0  0.0  0.0 0.0 0.0 0.0 -0.3 0.0  0.0 0.0 0.5 0.0  0.0  0.0
#> C 0.0  0.0 2.1  0.0  0.0 0.0 0.0 0.0  0.0 0.0  0.0 0.0 0.0 0.0  0.0  0.0
#> D 0.0  0.0 0.0  2.1  0.0 0.0 0.0 0.0 -0.6 0.0  0.0 0.0 0.0 0.0  0.0  0.0
#> E 0.0  0.0 0.0  0.0  2.1 0.0 0.0 0.0  0.0 0.0 -0.5 0.0 0.0 0.0  0.0  0.0
#> F 0.0  0.0 0.0  0.0  0.0 1.7 0.0 0.0  0.0 0.0  0.0 0.0 0.0 0.0  0.0  0.0
#> G 0.0  0.0 0.0  0.0  0.0 0.0 2.3 0.0  0.0 0.0  0.0 0.0 0.0 0.0  0.0  0.0
#> H 0.0  0.0 0.0  0.0  0.0 0.0 0.0 1.5  0.0 0.0  0.0 0.0 0.0 0.0  0.0  0.4
#> I 0.0 -0.3 0.0 -0.6  0.0 0.0 0.0 0.0  1.5 0.0  0.0 0.0 0.0 0.0 -0.4  0.0
#> J 0.5  0.0 0.0  0.0  0.0 0.0 0.0 0.0  0.0 2.1  0.0 0.5 0.0 0.0  0.0  0.0
#> K 0.0  0.0 0.0  0.0 -0.5 0.0 0.0 0.0  0.0 0.0  1.8 0.0 0.0 0.0 -0.5  0.0
#> L 0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0  0.0 0.5  0.0 1.6 0.0 0.0  0.0  0.0
#> M 0.0  0.5 0.0  0.0  0.0 0.0 0.0 0.0  0.0 0.0  0.0 0.0 1.8 0.0  0.0  0.0
#> N 0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0  0.0 0.0  0.0 0.0 0.0 2.3  0.0  0.0
#> O 0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 -0.4 0.0 -0.5 0.0 0.0 0.0  1.8 -0.5
#> P 0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.4  0.0 0.0  0.0 0.0 0.0 0.0 -0.5  1.6