# DESP_MST: Estimation of DESP using minimum spanning trees In DESP: Estimation of Diagonal Elements of Sparse Precision-Matrices

## Description

This function estimates the diagonal of the precision matrix by symmetry-enforced likelihood minimization using minimum spanning trees, when the true value of the coefficient matrix `B` is known or has already been estimated. The observations of the data matrix `X` are assumed to have zero mean.

## Usage

 `1` ``` DESP_MST(X, B, Theta = NULL) ```

## Arguments

 `X` The data matrix. `B` The coefficient matrix. `Theta` The matrix orresponding to outliers.

## Details

When Theta is not NULL, we consider an additive contamination model. We assume that X = Y + E is observed, denoting the outlier-free data by Y and the matrix of errors by E. In this case, the matrix Theta should be equal to E * B.

## Value

This function returns the diagonal of the precision matrix associated with X as a vector.

## Author(s)

Arnak Dalalyan and Samuel Balmand.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```## build the true precision matrix p <- 12 # number of variables Omega <- 2*diag(p) Omega[1,1] <- p Omega[1,2:p] <- 2/sqrt(2) Omega[2:p,1] <- 2/sqrt(2) ## compute the true diagonal of the precision matrix Phi <- 1/diag(Omega) ## generate the design matrix from a zero-mean Gaussian distribution require(MASS) n <- 100 # sample size X <- mvrnorm(n,rep.int(0,p),ginv(Omega)) ## compute the sample mean barX <- apply(X,2,mean) ## subtract the mean from all the rows X <- t(t(X)-barX) ## estimate the coefficient matrix B <- DESP_SRL_B(X,lambda=sqrt(2*log(p))) ## compute the squared partial correlations SPC <- DESP_SqPartCorr(B,n) ## re-estimate the coefficient matrix by ordinary least squares B_OLS <- DESP_OLS_B(X,SPC) ## estimate the diagonal of the precision matrix and get its inverse hatPhiMST <- 1/DESP_MST(X,B_OLS) ## measure the performance of the estimation using l2 vector norm sqrt(sum((Phi-hatPhiMST)^2)) ```

DESP documentation built on May 29, 2017, 9:27 p.m.