Description Usage Arguments Details Value Author(s) See Also Examples
An alternating optimization algorithm for estimation of precision matrices of sparse tensor graphical models. See Lyu et al. (2019) for details.
1 | Tlasso.fit(data, T = 1, lambda.vec = NULL, norm.type = 2, thres = 1e-05)
|
data |
tensor object stored in a m1 * m2 * ... * mK * n array, where n is sample size and mk is dimension of the kth tensor mode. |
T |
number of maximal iteration, default is 1. Each iteration involves update on all modes.
If output change less than |
lambda.vec |
vector of tuning parameters (λ_1,...,λ_K). Defalut is NULL, s.t. it is tuned via |
norm.type |
normalization method of precision matrix, i.e., Ω_{11}=1 if norm.type = 1 and ||Ω||_F =1 if norm.type = 2. Default value is 2. |
thres |
thresholding value that terminates algorithm before Tth iteration if output change less than |
This function conducts an alternating optimization algorithm to sparse tensor graphical model. The output is optimal consistent even when T=1
, see Lyu et al. (2019) for details.
There are two ternimation criteria, T
and thres
. Algorithm will be terminated if output in certain iteration change less than thres
. Otherwise, T iterations will be fully operated.
A length-K list of estimation of precision matrices.
Xiang Lyu, Will Wei Sun, Zhaoran Wang, Han Liu, Jian Yang, Guang Cheng.
1 2 3 4 5 6 7 8 9 10 11 | m.vec = c(5,5,5) # dimensionality of a tensor
n = 5 # sample size
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=10,lambda.vec = lambda.thm,thres=10)
# terminate by thres
out.tlasso = Tlasso.fit(DATA,T=3,lambda.vec = lambda.thm,thres=0)
# thres=0, iterate 10 times
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