tensor_regress {tensorregress}

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")