Estimation of DESP by average absolute deviation around the mean
This function estimates the diagonal of the precision matrix by residual variance 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.
The data matrix.
The coefficient matrix.
The matrix orresponding to outliers.
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.
This function returns the diagonal of the precision matrix associated with X as a vector.
Arnak Dalalyan and Samuel Balmand.
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## 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 hatPhiAD <- 1/DESP_AD(X,B_OLS) ## measure the performance of the estimation using l2 vector norm sqrt(sum((Phi-hatPhiAD)^2))
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