PMSE: Prediction and mean squared error.

In TRES: Tensor Regression with Envelope Structure

Description

Evaluate the tensor response regression (TRR) or tensor predictor regression (TPR) model through the mean squared error.

Usage

PMSE(x, y, B)

Arguments

x	A predictor tensor, array, matrix or vector.
y	A response tensor, array, matrix or vector.
B	An coefficient tensor tensor, array, matrix or vector.

Details

There are three situations:

• TRR model: If y is an m-way tensor (array), x should be matrix or vector and B should be tensor or array.

• TPR model: If x is an m-way tensor (array), y should be matrix or vector and B should be tensor or array.

• Other: If x and y are both matrix or vector, B should be matrix. In this case, the prediction is calculated as pred = B*X.

In any cases, users are asked to ensure the dimensions of x, y and B match. See TRRsim and TPRsim for more details of the TRR and TPR models.

Let \hat{Y}_i denote each prediction, then the mean squared error is defined as 1/n∑_{i=1}^n||Y_i-\hat{Y}_i||_F^2, where ||\cdot||_F denotes the Frobenius norm.

Value

mse	The mean squared error.
pred	The predictions.

See Also

TRRsim, TPRsim.

Examples

## Dataset in TRR model
r <- c(10, 10, 10)
u <- c(2, 2, 2)
p <- 5
n <- 100
dat <- TRRsim(r = r, p = p, u = u, n = n)
x <- dat$x
y <- dat$y

# Fit data with TRR.fit
fit_std <- TRR.fit(x, y, method="standard")
result <- PMSE(x, y, fit_std$coefficients)
## Dataset in TPR model
p <- c(10, 10, 10)
u <- c(1, 1, 1)
r <- 5
n <- 200
dat <- TPRsim(p = p, r = r, u = u, n = n)
x <- dat$x
y <- dat$y

# Fit data with TPR.fit
fit_std <- TPR.fit(x, y, u, method="standard")
result <- PMSE(x, y, fit_std$coefficients)

TRES documentation built on Oct. 20, 2021, 9:06 a.m.