space.joint: A function to estimate partial correlations using the Joint... In space: Sparse PArtial Correlation Estimation

Description

A function to estimate partial correlations using the Joint Sparse Regression Model

Usage

 1 space.joint(Y.m, lam1, lam2=0, sig=NULL, weight=NULL,iter=2)

Arguments

 Y.m numeric matrix. Columns are for variables and rows are for samples. Missing values are not allowed. It's recommended to first standardize each column to have mean 0 and l_2 norm 1. lam1 numeric value. This is the l_1 norm penalty parameter. If the columns of Y.m have norm one, then the suggested range of lam1 is: O(n^{3/2}Φ^{-1}(1-α/(2p^2))) for small α such as 0.1. lam2 numeric value. If not specified, lasso regression is used in the Joint Sparse Regression Model (JSRM). Otherwise, elastic net regression is used in JSRM and lam2 serves as the l_2 norm penalty parameter. sig numeric vector. Its length should be the same as the number of columns of Y.m. It is the vector of σ^{ii} (the diagonal of the inverse covariance matrix). If not specified, σ^{ii} will be estimated during the model fitting with initial values rep(1,p). The number of the iteration of the model fitting (iter) will then be at least 2. Note, the scale of sig does not matter. weight numeric value or vector. It specifies the weights or the type of weights used for each regression in JSRM. The default value is NULL, which means all regressions will be weighted equally in the joint model. If weight=1, residue variances will be used for weights. If weight=2, the estimated degree of each variable will be used for weights. Otherwise, it should be a positive numeric vector, whose length is equal to the number of columns of Y.m. iter integer. It is the total number of interactions in JSRM for estimating σ^{ii} and partial correlations. When sig=NULL and/or weight=NULL or 2, iter should be at least 2.

Details

space.joint uses a computationally efficient approach for selecting non-zero partial correlations under the high-dimension-low-sample-size setting (Peng and et.al., 2007).

Value

A list with two components

 ParCor the estimated partial correlation matrix. sig.fit numeric vector of the estimated diagonal σ^{ii}.

Author(s)

J. Peng, P. Wang, Nengfeng Zhou, Ji Zhu

References

J. Peng, P. Wang, N. Zhou, J. Zhu (2007), Partial Correlation Estimation by Joint Sparse Regression Model.

Meinshausen, N., and Buhlmann, P. (2006), High Dimensional Graphs and Variable Selection with the Lasso, Annals of Statistics, 34, 1436-1462.