sele_rank: Rank selection

In tensorregress: Supervised Tensor Decomposition with Side Information

Rank selection

Description

Estimate the Tucker rank of tensor decomposition based on BIC criterion. The choice of BIC aims to balance between the goodness-of-fit for the data and the degree of freedom in the population model.

Usage

sele_rank(
  tsr,
  X_covar1 = NULL,
  X_covar2 = NULL,
  X_covar3 = NULL,
  rank_range,
  niter = 10,
  cons = "non",
  lambda = 0.1,
  alpha = 1,
  solver = "CG",
  dist,
  initial = c("random", "QR_tucker")
)

Arguments

tsr	response tensor with 3 modes
X_covar1	side information on first mode
X_covar2	side information on second mode
X_covar3	side information on third mode
rank_range	a matrix containing rank candidates on each row
niter	max number of iterations if update does not convergence
cons	the constraint method, "non" for without constraint, "vanilla" for global scale down at each iteration, "penalty" for adding log-barrier penalty to object function.
lambda	penalty coefficient for "penalty" constraint
alpha	max norm constraint on linear predictor
solver	solver for solving object function when using "penalty" constraint, see "details"
dist	distribution of response tensor, see "details"
initial	initialization of the alternating optimiation, "random" for random initialization, "QR_tucker" for deterministic initialization using tucker decomposition

Details

For rank selection, recommend using non-constraint version.

Constraint penalty adds log-barrier regularizer to general object function (negative log-likelihood). The main function uses solver in function "optim" to solve the objective function. The "solver" passes to the argument "method" in function "optim".

dist specifies three distributions of response tensor: binary, poisson and normal distributions.

Value

a list containing the following:

rank a vector with selected rank with minimal BIC

result a matrix containing rank candidate and its loglikelihood and BIC on each row

Examples

seed=24
dist='binary'
data=sim_data(seed, whole_shape = c(20,20,20),
core_shape=c(3,3,3),p=c(5,5,5),dist=dist, dup=5, signal=4)
rank_range = rbind(c(3,3,3),c(3,3,2),c(3,2,2),c(2,2,2),c(3,2,3))
re = sele_rank(data$tsr[[1]],data$X_covar1,data$X_covar2,data$X_covar3,
 rank_range = rank_range,niter=10,cons = 'non',dist = dist,initial = "random")

tensorregress documentation built on July 9, 2023, 7:23 p.m.