The goal ofgrasps is to provide a collection ofstatistical methods that incorporate both element-wise and group-wisepenalties to estimate a precision matrix, making them user-friendly anduseful for researchers and practitioners.
\[\hat{\Omega}(\lambda,\alpha,\gamma) ={\arg\min}_{\Omega \succ 0}\{ -\log\det(\Omega) + \text{tr}(S\Omega) + \lambdaP_{\alpha,\gamma}(\Omega) \},\]
\[P_{\alpha,\gamma}(\Omega)= \alpha P^\text{idv}_\gamma(\Omega) + (1-\alpha)P^\text{grp}_\gamma(\Omega),\]
\[P^\text{idv}_\gamma(\Omega) = \sum_{i,j}p_\gamma(\vert\omega_{ij}\vert),\]
\[P^\text{grp}_\gamma(\Omega)= \sum_{g,g^\prime}p_\gamma(\Vert\Omega_{gg^\prime}\Vert_F).\]
For more details, see the vignettePenalizedPrecision Matrix Estimation in grasps.
The packagegrasps provides functions to estimateprecision 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 vignettePenalizedPrecision Matrix Estimation in grasps for more details.
You can install the development version ofgraspsfromGitHub with:
# install.packages("devtools")devtools::install_github("Carol-seven/grasps")library(grasps)## reproducibility for everythingset.seed(1234)## block-structured precision matrix based on SBMsim<-gen_prec_sbm(d =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)## synthetic datalibrary(MASS)X<-mvrnorm(n =20,mu =rep(0,30),Sigma = sim$Sigma)## solutionres<-grasps(X = X,membership = sim$membership,penalty ="adapt",crit ="HBIC")## visualizationplot(res)
## performanceperformance(hatOmega = res$hatOmega,Omega = sim$Omega)#> measure value#> 1 sparsity 0.9103#> 2 Frobenius 24.6796#> 3 KL 7.2063#> 4 quadratic 54.1949#> 5 spectral 13.1336#> 6 TP 22.0000#> 7 TN 370.0000#> 8 FP 17.0000#> 9 FN 26.0000#> 10 TPR 0.4583#> 11 FPR 0.0439#> 12 F1 0.5057#> 13 MCC 0.4545