# ChainOmega: Precision Matrix of Triangle Graph In Tlasso: Non-Convex Optimization and Statistical Inference for Sparse Tensor Graphical Models

## Description

Generate precision matrix of triangle graph (chain like network) following the set-up in Fan et al. (2009).

## Usage

 `1` ```ChainOmega(p, sd = 1, norm.type = 2) ```

## Arguments

 `p` dimension of generated precision matrix. `sd` seed for random number generation, default is 1. `norm.type` normalization methods of generated precision matrix, i.e., Ω_{11}=1 if norm.type = 1 and ||Ω||_F =1 if norm.type = 2. Default value is 2.

## Details

This function first construct a covariance matrix Σ that its (i,j) entry is exp (- | h_i - h_j | / 2) with h_1 < h_2 < … < h_p. The difference h_i - h_{i+1} is generated i.i.d. from Unif(0.5,1). See Fan et al. (2009) for more details.

## Value

A precision matrix generated from triangle graph.

## Author(s)

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

`NeighborOmega`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```m.vec = c(5,5,5) # dimensionality of a tensor n = 5 # sample size Omega.true.list = list() for ( k in 1:length(m.vec)){ Omega.true.list[[k]] = ChainOmega(m.vec[k],sd=k*100,norm.type=2) } Omega.true.list # a list of length 3 contains precision matrices from triangle graph ```

Tlasso documentation built on May 29, 2017, 5:59 p.m.