TRES (version 0.1.0)

FG_TRR: Envelope estimation of tensor response regression with the full Grassmannian optimization

Description

This function is used for envelope estimation of tensor response regression with the full Grassmannian (FG) optimization.

Usage

FG_TRR(Yn, Xn, Gamma_init)

Arguments

Yn

The response tensor instance or dimension \(r_1\times r_2\times\cdots\times r_m \times n\), where \(n\) is the sample size.

Xn

The predictor matrix of dimension \(p \times n\).

Gamma_init

The initial estimation of envelope subspace basis, can be derived from TRR.

Value

Bhat

The estimation of regression coefficient tensor.

Gamma_hat

The FG estimation of envelope subspace basis.

Examples

# NOT RUN {
rm(list=ls())

r <- c(10, 10, 10)
m <- length(r)
u <- c(2, 2, 2)
p <- 5
n <- 100


set.seed(1)
eta <- array(runif(prod(u)*p), c(u, p))
eta <- as.tensor(eta)

Gamma <- Gamma0 <- Omega <- Omega0 <- Sig <- Sigsqrtm <- NULL
for (i in 1:m){
  tmp <- matrix(runif(r[i]*u[i]), r[i], u[i])
  Gamma[[i]] <- qr.Q(qr(tmp))
  Gamma0[[i]] <- qr.Q(qr(Gamma[[i]]),complete=TRUE)[,(u[i]+1):r[i]]

  A <- matrix(runif(u[i]^2), u[i], u[i])
  Omega[[i]] <- A %*% t(A)
  A <- matrix(runif((r[i]-u[i])^2), (r[i]-u[i]), (r[i]-u[i]))
  Omega0[[i]] <- A %*% t(A)
  Sig[[i]] <- Gamma[[i]] %*% Omega[[i]] %*% t(Gamma[[i]])+
    Gamma0[[i]] %*% Omega0[[i]] %*% t(Gamma0[[i]])
  Sig[[i]] <- 10*Sig[[i]]/norm(Sig[[i]], type="F")+0.01*diag(r[i])
  Sigsqrtm[[i]] <- pracma::sqrtm(Sig[[i]])$B
}
B <- ttl(eta, Gamma, ms=1:m)
Xn <- matrix(rnorm(p*n), p, n)
Xn_inv <- MASS::ginv(Xn %*% t(Xn)) %*% Xn
Epsilon <- array(rnorm(prod(r)*n), c(r, n))
Epsilon <- as.tensor(Epsilon)
Epsilon <- ttl(Epsilon, Sigsqrtm, ms=1:m)
Yn <- Epsilon + ttm(B, t(Xn), m+1)


res_1D = TRR(Yn, Xn, u, method="1D")
res_FG = FG_TRR(Yn, Xn, Gamma_init=res_1D$Gamma_hat)

rTensor::fnorm(B-res_1D$Bhat)
rTensor::fnorm(B-res_FG$Bhat)
# }