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 Sun et al. (2016) 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 ( |

`norm.type` |
normalization method of precision matrix, i.e., |

`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 Sun et al. (2016) 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.

Will Wei Sun, Zhaoran Wang, Xiang Lyu, Han Liu, 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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