ALC | R Documentation |
Acts on a gp
, dgp2
, or dgp3
object.
Current version requires squared exponential covariance
(cov = "exp2"
). Calculates ALC over the input locations
x_new
using specified reference grid. If no reference grid is
specified, x_new
is used as the reference. Optionally utilizes
SNOW parallelization. User should
select the point with the highest ALC to add to the design.
ALC(object, x_new, ref, cores)
## S3 method for class 'gp'
ALC(object, x_new = NULL, ref = NULL, cores = 1)
## S3 method for class 'dgp2'
ALC(object, x_new = NULL, ref = NULL, cores = 1)
## S3 method for class 'dgp3'
ALC(object, x_new = NULL, ref = NULL, cores = 1)
object |
object of class |
x_new |
matrix of possible input locations, if object has been run
through |
ref |
optional reference grid for ALC approximation, if |
cores |
number of cores to utilize in parallel, by default no parallelization is used |
Not yet implemented for Vecchia-approximated fits.
All iterations in the object are used in the calculation, so samples
should be burned-in. Thinning the samples using trim
will
speed up computation. This function may be used in two ways:
Option 1: called on an object with only MCMC iterations, in
which case x_new
must be specified
Option 2: called on an object that has been predicted over, in
which case the x_new
from predict
is used
In Option 2, it is recommended to set store_latent = TRUE
for
dgp2
and dgp3
objects so
latent mappings do not have to be re-calculated. Through predict
,
the user may specify a mean mapping (mean_map = TRUE
) or a full
sample from the MVN distribution over w_new
(mean_map = FALSE
). When the object has not yet been predicted
over (Option 1), the mean mapping is used.
SNOW parallelization reduces computation time but requires more memory storage. C code derived from the "laGP" package (Robert B Gramacy and Furong Sun).
list with elements:
value
: vector of ALC values, indices correspond to x_new
time
: computation time in seconds
Sauer, A., Gramacy, R.B., & Higdon, D. (2023). Active learning for deep
Gaussian process surrogates. *Technometrics, 65,* 4-18. arXiv:2012.08015
Seo, S, M Wallat, T Graepel, and K Obermayer. 2000. Gaussian Process Regression:
Active Data Selection and Test Point Rejection. In Mustererkennung 2000,
2734. New York, NY: SpringerVerlag.
Gramacy, RB and F Sun. (2016). laGP: Large-Scale Spatial Modeling via Local
Approximate Gaussian Processes in R. Journal of Statistical Software
72 (1), 1-46. doi:10.18637/jss.v072.i01
# --------------------------------------------------------
# Example 1: toy step function, runs in less than 5 seconds
# --------------------------------------------------------
f <- function(x) {
if (x <= 0.4) return(-1)
if (x >= 0.6) return(1)
if (x > 0.4 & x < 0.6) return(10*(x-0.5))
}
x <- seq(0.05, 0.95, length = 7)
y <- sapply(x, f)
x_new <- seq(0, 1, length = 100)
# Fit model and calculate ALC
fit <- fit_two_layer(x, y, nmcmc = 100, cov = "exp2")
fit <- trim(fit, 50)
fit <- predict(fit, x_new, cores = 1, store_latent = TRUE)
alc <- ALC(fit)
# --------------------------------------------------------
# Example 2: damped sine wave
# --------------------------------------------------------
f <- function(x) {
exp(-10*x) * (cos(10*pi*x - 1) + sin(10*pi*x - 1)) * 5 - 0.2
}
# Training data
x <- seq(0, 1, length = 30)
y <- f(x) + rnorm(30, 0, 0.05)
# Testing data
xx <- seq(0, 1, length = 100)
yy <- f(xx)
plot(xx, yy, type = "l")
points(x, y, col = 2)
# Conduct MCMC (can replace fit_two_layer with fit_one_layer/fit_three_layer)
fit <- fit_two_layer(x, y, D = 1, nmcmc = 2000, cov = "exp2")
plot(fit)
fit <- trim(fit, 1000, 2)
# Option 1 - calculate ALC from MCMC iterations
alc <- ALC(fit, xx)
# Option 2 - calculate ALC after predictions
fit <- predict(fit, xx, cores = 1, store_latent = TRUE)
alc <- ALC(fit)
# Visualize fit
plot(fit)
par(new = TRUE) # overlay ALC
plot(xx, alc$value, type = 'l', lty = 2,
axes = FALSE, xlab = '', ylab = '')
# Select next design point
x_new <- xx[which.max(alc$value)]
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