errorMeasureRegress: Error Measures for GP Models.

In lineqGPR: Gaussian Process Regression Models with Linear Inequality Constraints

Description

Compute error measures for GP models: mean absulte error ("mae"), mean squared error ("mse"), standardised mse ("smse"), mean standardised log loss ("msll"), Q2 ("q2"), predictive variance adequation ("pva"), confidence interval accuracy ("cia").

Usage

errorMeasureRegress(
  y,
  ytest,
  mu,
  varsigma,
  type = "all",
  control = list(nsigma = 1.96)
)

Arguments

y	a vector with the output observations used for training.
ytest	a vector with the output observations used for testing.
mu	a vector with the posterior mean.
varsigma	a vector with the posterior variances.
type	a character string corresponding to the type of the measure.
control	an optional list with parameters to be passed (e.g. cia: "nsigma").

Value

The values of the error measures.

Author(s)

A. F. Lopez-Lopera.

References

Rasmussen, C. E. and Williams, C. K. I. (2005), "Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)". The MIT Press. [link]

Bachoc, F. (2013), "Cross validation and maximum likelihood estimations of hyper-parameters of Gaussian processes with model misspecification". Computational Statistics & Data Analysis, 66:55-69. [link]

See Also

errorMeasureRegressMC

Examples

# generating the toy example
n <- 100
w <- 4*pi
x <- seq(0, 1, length = n)
y <- sin(w*x)

# results with high-level noises generating the toy example
nbsamples <- 100
set.seed(1)
ynoise <- y + matrix(rnorm(n*nbsamples, 0, 10), ncol = nbsamples)
mu <- apply(ynoise, 1, mean)
sigma <- apply(ynoise, 1, sd)
matplot(x, ynoise, type = "l", col = "gray70")
lines(x, y, lty = 2, col = "red")
lines(x, mu, col = "blue")
lines(x, mu+1.98*sigma, lty = 2)
lines(x, mu-1.98*sigma, lty = 2)
legend("topright", c("target", "mean", "confidence", "samples"),
       lty = c(2,1,2,1), col = c("red", "blue", "black", "gray70"))
t(errorMeasureRegress(y, y, mu, sigma^2))

# results with low-level noises generating the toy example
set.seed(1)
ynoise <- y + matrix(rnorm(n*nbsamples, 0, 0.05), ncol = nbsamples)
mu <- apply(ynoise, 1, mean)
sigma <- apply(ynoise, 1, sd)
matplot(x, ynoise, type = "l", col = "gray70")
lines(x, y, lty = 2, col = "red")
lines(x, mu, col = "blue")
lines(x, mu+1.98*sigma, lty = 2)
lines(x, mu-1.98*sigma, lty = 2)
legend("topright", c("target", "mean", "confidence", "samples"),
       lty = c(2,1,2,1), col = c("red", "blue", "black", "gray70"))
t(errorMeasureRegress(y, y, mu, sigma^2))

lineqGPR documentation built on Jan. 11, 2020, 9:23 a.m.