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The goal of grasps is to provide a collection of statistical methods that incorporate both element-wise and group-wise penalties to estimate a precision matrix, making them user-friendly and useful for researchers and practitioners.
\[ \hat{\Omega}(\lambda,\alpha,\gamma) = {\arg\min}_{\Omega \succ 0} \{ -\log\det(\Omega) + \text{tr}(S\Omega) + \mathcal{P}_{\lambda,\alpha,\gamma}(\Omega) \}, \] \[ \mathcal{P}_{\lambda,\alpha,\gamma}(\Omega) = \alpha \mathcal{P}^\text{idv}_{\lambda,\gamma}(\Omega) + (1-\alpha) \mathcal{P}^\text{grp}_{\lambda,\gamma}(\Omega), \] \[ \mathcal{P}^\text{idv}_{\lambda,\gamma}(\Omega) = \sum_{i,j} P_{\lambda,\gamma}(\lvert\omega_{ij}\rvert), \] \[ \mathcal{P}^\text{grp}_{\lambda,\gamma}(\Omega) = \sum_{g,g^\prime} P_{\lambda,\gamma}(\lVert\Omega_{gg^\prime}\rVert_F). \]
For more details, see the vignette Penalized Precision Matrix Estimation in grasps.
The package grasps provides functions to estimate precision matrices using the following penalties:
| Penalty | Reference |
|---|---|
Lasso
(penalty = "lasso") |
Tibshirani (1996); Friedman et al. (2008) |
Adaptive lasso
(penalty = "adapt") |
Zou (2006); Fan et al. (2009) |
Atan (penalty = "atan") |
Wang and Zhu (2016) |
Exp (penalty = "exp") |
Wang et al. (2018) |
Lq (penalty = "lq") |
Frank and Friedman (1993); Fu (1998); Fan and Li (2001) |
LSP (penalty = "lsp") |
Candès et al. (2008) |
MCP (penalty = "mcp") |
Zhang (2010) |
SCAD (penalty = "scad") |
Fan and Li (2001); Fan et al. (2009) |
See the vignette Penalized Precision Matrix Estimation in grasps for more details.
install.packages("grasps")# install.packages("pak")
pak::pkg_install("Carol-seven/grasps")library(grasps)
## reproducibility for everything
set.seed(1234)
## block-structured precision matrix based on SBM
sim <- gen_prec_sbm(p = 30, K = 3,
within.prob = 0.25, between.prob = 0.05,
weight.dists = list("gamma", "unif"),
weight.paras = list(c(shape = 20, rate = 10),
c(min = 0, max = 5)),
cond.target = 100)
## ground truth visualization
plot(sim)
## n-by-p data matrix
library(MASS)
X <- mvrnorm(n = 20, mu = rep(0, 30), Sigma = sim$Sigma)
## precision matrix: adaptive lasso; BIC
prec <- grasps(X = X, membership = sim$membership, penalty = "adapt", crit = "BIC")
## precision matrix visualization
plot(prec)
## performance
performance(hatOmega = prec$hatOmega, Omega = sim$Omega)
#> measure value
#> 1 sparsity 0.8805
#> 2 Frobenius 23.9013
#> 3 KL 7.6775
#> 4 quadratic 69.1639
#> 5 spectral 12.3571
#> 6 TP 23.0000
#> 7 TN 358.0000
#> 8 FP 29.0000
#> 9 FN 25.0000
#> 10 TPR 0.4792
#> 11 FPR 0.0749
#> 12 F1 0.4600
#> 13 MCC 0.3904
## adjacency matrix: diagonal = 0; raw partial correlations;
## no thresholding; weighted network
adj <- prec_to_adj(prec$hatOmega,
diag.zero = TRUE, absolute = FALSE,
threshold = NULL, weighted = TRUE)
## adjacency matrix visualization
plot(adj)
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.