Precision Matrix of Triangle Graph

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Description

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

Usage

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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.

See Also

NeighborOmega

Examples

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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