knitr::opts_chunk$set( collapse = TRUE, comment = "#>", # fig.path = "README-" fig.path = "tools/README-" ) set.seed(0)
The goal of CGGP is to provide a sequential design of experiment algorithm that can efficiently use many points and interpolate exactly.
You can install CGGP from GitHub with:
# install.packages("devtools") devtools::install_github("CollinErickson/CGGP")
To create a CGGP object:
## basic example code library(CGGP) d <- 4 CG <- CGGPcreate(d=d,200) print(CG)
A new CGGP
object has design points that should be evaluated next, either from CG$design
or CG$design_unevaluated
.
f <- function(x) {x[1]^2*cos(x[3]) + 4*(0.5-x[2])^3*(1-x[1]/3) + x[1]*sin(2*2*pi*x[3]^2)} Y <- apply(CG$design, 1, f)
Once you have evaluated the design points, you can fit the object with CGGPfit
.
set.seed(1)
CG <- CGGPfit(CG, Y) CG
If you want to use the model to make predictions at new input points,
you can use CGGPpred
.
xp <- matrix(runif(10*CG$d), ncol=CG$d) CGGPpred(CG, xp)
To add new design points to the already existing design,
use CGGPappend
.
It will use the data already collected to find the most
useful set of points to evaluate next.
set.seed(1)
# To add 100 points CG <- CGGPappend(CG, 100)
Now you will need to evaluate the points added to CG$design
,
and refit the model.
set.seed(1)
ynew <- apply(CG$design_unevaluated, 1, f) CG <- CGGPfit(CG, Ynew=ynew)
set.seed(0)
There are a few functions that will help visualize the CGGP design.
CGGPplotblocks
CGGPplotblocks
shows the block structure when projected down
to all pairs of two dimensions.
The plot is symmetric.
The facet labels be a little bit confusing.
The first column has the label 1, and it looks like it is saying that
the x-axis for each plot in that column is for X1
, but it is
actually the y-axis that is X1
for each plot in that column.
CGGPplotblocks(CG)
CGGPplotheat
CGGPplotheat
is similar to CGGPplotblocks
and can be easier to read
since it is only a single plot.
The $(i,j)$ entry shows the maximum value for which a block was selected
with $X_i$ and $X_j$ at least that large.
The diagonal entries, $(i, i)$, show the maximum depth for $X_i$.
A diagonal entry must be at least as large as any entry in its column or row.
This plot is also symmetric.
CGGPplotheat(CG)
CGGPhist
CGGPhist
shows histograms of the block depth in each direction.
The dimensions that have more large values are dimensions that have been
explored more.
These should be the more active dimensions.
CGGPplothist(CG)
CGGPplotcorr
CGGPplotcorr
gives an idea of what the correlation structure in each
dimension is.
The values plotted do not represent the actual data given to CGGP.
Each wiggly line represents a random Gaussian process drawn using the
correlation parameters for that dimension from the given CGGP model.
Dimensions that are more wiggly and have higher variance are the
more active dimensions.
Dimensions with nearly flat lines mean that the corresponding input
dimension has a relatively small effect on the output.
CGGPplotcorr(CG)
CGGPplotvariogram
CGGPplotvariogram
shows something similar to the semi-variogram
for the correlation parameters found for each dimension.
Really it is just showing how the correlation function decays for
points that are further away.
It should always start at y=1
for x=0
and decrease in y
as x
gets larger
CGGPplotvariogram(CG)
CGGPplotslice
CGGPplotslice
shows what the predicted model along each individual
dimension when the other input dimensions are held constant, i.e.,
a slice along a single dimension.
By default the slice is done holding all other inputs at 0.5, but this
can be changed by changing the argument proj
.
The black dots are the data points that are in that slice
If you change proj
to have values not equal to 0.5, you probably
won't see any black dots.
The pink regions are the 95% prediction intervals.
This plot is the best for giving an idea of what the higher dimension function look like. You can see how the output changes as each input is varied.
CGGPplotslice(CG)
The next plot changes so that all the other dimensions are held constant at 0.15 for each slice plot. When moving from the center line, the error bounds generally should be larger since it is further from the data, but we should see similar patterns unless the function is highly nonlinear.
CGGPplotslice(CG, proj = rep(.15, CG$d))
CGGPplottheta
CGGPplottheta
is useful for getting an idea of how the
samples for the correlation parameters (theta) vary compared
to the maximum a posteriori (MAP).
This may be helpful when using UCB
or TS
in CGGPappend
to get an idea of how much uncertainty there is in the
parameters.
Note that there are likely multiple parameters for each input dimension.
CGGPplottheta(CG)
CGGPplotsamplesneglogpost
CGGPplotsamplesneglogpost
shows the negative log posterior
for each of the different samples for theta.
The value for the MAP is shown as a blue line.
It should be at the far left edge if it is the true MAP.
CGGPplotsamplesneglogpost(CG)
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