TRES (version 1.1.3)

FG_TRR-deprecated: Envelope estimation of tensor response regression (TRR) 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(Xn, Yn, Gamma_init)

Arguments

Xn

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

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.

Gamma_init

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

Value

Bhat

The estimation of regression coefficient tensor.

Gamma_hat

The FG estimation of envelope subspace basis.

See Also

TRES-deprecated

Examples

# NOT RUN {
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 <- rTensor::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 <- rTensor::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 <- rTensor::as.tensor(Epsilon)
Epsilon <- rTensor::ttl(Epsilon, Sigsqrtm, ms=1:m)
Yn <- Epsilon + rTensor::ttm(B, t(Xn), m+1)

# use the result of 1D method as the initial value
res_1D = TRR.fit(Xn, Yn, u, method="1D")
# }
# NOT RUN {
  res_FG = FG_TRR(Xn, Yn, Gamma_init=res_1D$Gamma_hat)
# }