tensor_regress: Supervised Tensor Decomposition with Interactive Side...

In tensorregress: Supervised Tensor Decomposition with Side Information

Supervised Tensor Decomposition with Interactive Side Information

Description

Supervised tensor decomposition with interactive side information on multiple modes. Main function in the package. The function takes a response tensor, multiple side information matrices, and a desired Tucker rank as input. The output is a rank-constrained M-estimate of the core tensor and factor matrices.

Usage

tensor_regress(
  tsr,
  X_covar1 = NULL,
  X_covar2 = NULL,
  X_covar3 = NULL,
  core_shape,
  niter = 20,
  cons = c("non", "vanilla", "penalty"),
  lambda = 0.1,
  alpha = 1,
  solver = "CG",
  dist = c("binary", "poisson", "normal"),
  traj_long = FALSE,
  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
core_shape	the Tucker rank of the tensor decomposition
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 the response tensor, see "details"
traj_long	if "TRUE", set the minimal iteration number to 8; if "FALSE", set the minimal iteration number to 0
initial	initialization of the alternating optimiation, "random" for random initialization, "QR_tucker" for deterministic initialization using tucker decomposition

Details

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 distribution.

If dist is set to "normal" and initial is set to "QR_tucker", then the function returns the results after initialization.

Value

a list containing the following:

W a list of orthogonal factor matrices - one for each mode, with the number of columns given by core_shape

G an array, core tensor with the size specified by core_shape

C_ts an array, coefficient tensor, Tucker product of G,A,B,C

U linear predictor,i.e. Tucker product of C_ts,X_covar1,X_covar2,X_covar3

lglk a vector containing loglikelihood at convergence

sigma a scalar, estimated error variance (for Gaussian tensor) or dispersion parameter (for Bernoulli and Poisson tensors)

violate a vector listing whether each iteration violates the max norm constraint on the linear predictor, 1 indicates violation

Examples

seed = 34
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)
re = tensor_regress(data$tsr[[1]],data$X_covar1,data$X_covar2,data$X_covar3,
core_shape=c(3,3,3),niter=10, cons = 'non', dist = dist,initial = "random")

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