est.analysis: Estimation Errors and TPR/TNR In Tlasso: Non-Convex Optimization and Statistical Inference for Sparse Tensor Graphical Models

Description

Compute estimation errors and TPR/TNR of optimization for sparse tensor graphical models

Usage

 `1` ```est.analysis(Omega.hat.list, Omega.true.list, offdiag = TRUE) ```

Arguments

 `Omega.hat.list` list of estimation of precision matrices of tensor, i.e., `Omega.hat.list[[k]]` is estimation of precision matrix for the kth tensor mode, 1 <= k <= K . For example, output of `Tlasso.fit`. `Omega.true.list` list of true precision matrices of tensor, i.e., `Omega.true.list[[k]]` is true precision matrix for the kth tensor mode, 1 <= k <= K . `offdiag` logical; indicate if excludes diagnoal when computing performance measures. If `offdiag = TRUE`, diagnoal in each matrix is ingored when comparing two matrices. Default is `TRUE`.

Details

This function computes performance measures of optimazation for sparse tensor graphical models. Errors are measured in Frobenius norm and Max norm. Model selection measures are TPR and TNR. All these measures are computed in each mode, average across all modes, and kronecker production of precision matrices.

Value

A list, named `Out`, of following performance measures:

 `Out\$error.kro` error in Frobenius norm of kronecker product `Out\$tpr.kro` TPR of kronecker product `Out\$tnr.kro` TNR of kronecker product `Out\$av.error.f` averaged Frobenius norm error across all modes `Out\$av.error.max` averaged Max norm error across all modes `Out\$av.tpr` averaged TPR across all modes `Out\$av.tnr` averaged TNR across all modes `Out\$error.f` vector; error in Frobenius norm of each mode `Out\$error.max` vector; error in Max norm of each mode `Out\$tpr` vector; TPR of each mode `Out\$tnr` vector; TNR of each mode

Author(s)

Will Wei Sun, Zhaoran Wang, Xiang Lyu, Han Liu, Guang Cheng.

`Tlasso.fit`, `NeighborOmega`, `ChainOmega`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```m.vec = c(5,5,5) # dimensionality of a tensor n = 5 # sample size k=1 # index of interested mode Omega.true.list = list() Omega.true.list[[1]] = ChainOmega(m.vec[1], sd = 1) Omega.true.list[[2]] = ChainOmega(m.vec[2], sd = 2) Omega.true.list[[3]] = ChainOmega(m.vec[3], sd = 3) lambda.thm = 20*c( sqrt(log(m.vec[1])/(n*prod(m.vec))), sqrt(log(m.vec[2])/(n*prod(m.vec))), sqrt(log(m.vec[3])/(n*prod(m.vec)))) DATA=Trnorm(n,m.vec,type='Chain') # obersavations from tensor normal distribution out.tlasso = Tlasso.fit(DATA,T=1,lambda.vec = lambda.thm) # output is a list of estimation of precision matrices est.analysis(out.tlasso, Omega.true.list, offdiag=TRUE) # generate a list of performance measures ```