TRES (version 1.1.3)

FG_TPR-deprecated: Envelope estimation of tensor predictor regression (TPR) with the full Grassmannian optimization

Description

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

Usage

FG_TPR(Xn, Yn, Gamma_init)

Arguments

Xn

The predictor tensor instance or dimension \(p_1\times p_2\times\cdots\times p_m \times n\), where \(n\) is the sample size.

Yn

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

Gamma_init

The initial estimation of envelope subspace basis, can be derived from TPR.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 {
rm(list = ls())
p <- c(10, 10, 10)
u <- c(1, 1, 1)
m <- 3; r <- 5; n <- 200
eta <- array(runif(prod(u,r)), c(u,r))
eta <- rTensor::as.tensor(eta)

Gamma <- Gamma0 <- Omega <- Omega0 <- Sig <- Sigsqrtm <- NULL
for(i in 1:m) {
  tmp <- matrix(runif(p[i]*u[i]), p[i], u[i])
  Gamma[[i]] <- qr.Q(qr(tmp))
  Gamma0[[i]] <- qr.Q(qr(tmp), complete=TRUE)[, (u[i]+1):p[i]]
  Omega[[i]] <- diag(u[i])
  Omega0[[i]] <- 0.01*diag(p[i]-u[i])
  Sig[[i]] <- Gamma[[i]] %*% Omega[[i]] %*% t(Gamma[[i]])+
    Gamma0[[i]] %*% Omega0[[i]] %*% t(Gamma0[[i]])
  Sig[[i]] <- 2*Sig[[i]]/norm(Sig[[i]], type="F")
  Sigsqrtm[[i]] <- pracma::sqrtm(Sig[[i]])$B
}

B <- rTensor::ttl(eta,Gamma, ms = c(1:m))
A <- matrix(runif(r^2), r, r)
SigY <- A %*% t(A)
SigY <- SigY/norm(SigY, type="F")
##generate data
Epsilon <- MASS::mvrnorm(n, mu=rep(0, r), Sigma=SigY)
tmp2 <- array(rnorm(prod(p, n)), c(p, n))
Xn <- rTensor::as.tensor(tmp2)
Xn <- rTensor::ttl(Xn, Sigsqrtm, ms = c(1:m))
vecXn <- matrix(Xn@data, prod(p), n)
Y_tmp <- matrix(NA, r, n)
tmp <- array(NA, c(p, r))
for (j in 1:n) {
  for (s in 1:r) {
    tmp[, , , s] <-  B@data[, , , s]*Xn@data[, , , j]
  }
  Y_tmp[, j] <- apply(tmp, 4, sum)
}
Yn <-  Y_tmp + t(Epsilon)

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