tgp {tgp} | R Documentation |
A generic interface to treed Gaussian process models used by
many of the functions of class "tgp"
:
bgpllm
, btlm
,
blm
, bgp
, btgpllm
bgp
,
and plot.tgp
, tgp.trees
.
This more complicated interface is provided for a finer control of the model
parameterization.
tgp(X, Z, XX = NULL, BTE = c(2000, 7000, 2), R = 1, m0r1 = FALSE, linburn = FALSE, params = NULL, pred.n = TRUE, ds2x = FALSE, ego = FALSE, traces = FALSE, verb = 1)
X |
data.frame , matrix , or vector of inputs X |
Z |
Vector of output responses Z of length equal to the
leading dimension (rows) of X |
XX |
Optional data.frame , matrix , or vector of
predictive input locations with the same number of columns as X |
BTE |
3-vector of Monte-carlo parameters (B)urn in, (T)otal, and (E)very. Predictive samples are saved every E MCMC rounds starting at round B, stopping at T. |
R |
Number of repeats or restarts of BTE MCMC rounds, default
R=1 is no restarts |
m0r1 |
If TRUE the responses Z will be scaled to have a mean of
zero and a range of 1; default is FALSE |
linburn |
If TRUE initializes MCMC with B (additional)
rounds of Bayesian linear CART (bcart ); default is FALSE |
params |
Generic parameters list which can be provided for a more flexible model.
See tgp.default.params for more details about the parameter list |
pred.n |
TRUE (default) value results in prediction at the inputs
X ; FALSE skips prediction at X resulting in
a faster implementation |
ds2x |
TRUE results in ALC (Active Learning–Cohn) computation of expected
reduction in uncertainty calculations at the XX locations, which can be used
for adaptive sampling; FALSE (default) skips this computation, resulting in
a faster implementation |
ego |
TRUE results in EGO (Expected Global Optimization)
computation of expected information about the location of the minimum
reduction in uncertainty calculations at the XX locations, which can be used
for adaptive sampling; FALSE (default) skips this computation, resulting in
a faster implementation |
traces |
TRUE results in a saving of samples from the
posterior distribution for most of the parameters in the model. The
default is FALSE for speed/storage reasons. See note below |
verb |
Level of verbosity of R-console print statements: from 0 (none); 1 (default) which shows the “progress meter”; 2 includes an echo of initialization parameters; up to 3 and 4 (max) with more info about successful tree operations. |
tgp
returns an object of class "tgp"
. The function plot.tgp
can be used to help visualize results.
An object of type "tgp"
is a list containing at least the following
components... The final two (parts
& trees
) are
tree-related outputs unique to the T (tree) class functions– those which
have a positive first (alpha) parameter in
params$tree <- c(alpha, beta, minpart
.
Tree viewing is supported by tgp.trees
.
state |
unsigned short[3] random number seed to C |
X |
Input argument: data.frame of inputs X |
n |
Number of rows in X , i.e., dim(X)[1] |
d |
Number of cols in X , i.e., dim(X)[2] |
Z |
Vector of output responses Z |
XX |
Input argument: data.frame of predictive locations XX |
nn |
Number of rows in XX , i.e., dim(XX)[1] |
BTE |
Input argument: Monte-carlo parameters |
R |
Input argument: restarts |
linburn |
Input argument: initialize MCMC with linear CART |
params |
list of model parameters generated by
tgp.default.params |
dparams |
Double-representation of model input parameters used by C-code |
Zp.mean |
Vector of mean predictive estimates at X locations |
Zp.q1 |
Vector of 5% predictive quantiles at X locations |
Zp.q2 |
Vector of 95% predictive quantiles at X locations |
Zp.q |
Vector of quantile norms Zp.q2 - Zp.q1 |
ZZ.q1 |
Vector of 5% predictive quantiles at XX locations |
ZZ.q2 |
Vector of 95% predictive quantiles at XX locations |
ZZ.q |
Vector of quantile norms ZZ.q2 - ZZ.q1 , used by the
Active Learning–MacKay (ALM) adaptive sampling algorithm |
Ds2x |
If argument ds2x=TRUE , this vector contains ALC
statistics for XX locations |
ego |
If argument ego=TRUE , this vector contains EGO
statistics for XX locations |
response |
Name of response Z if supplied by data.frame
in argument, or “z” if none provided |
parts |
Internal representation of the regions depicted by partitions of the maximum a' posteriori (MAP) tree |
trees |
list of trees (maptree representation) which
were MAP as a function of each tree height sampled between MCMC
rounds B and T |
traces |
list containing traces of most of the model
parameters and posterior predictive distributions at input locations
XX . See note below |
verb |
Input argument: verbosity level |
Inputs X, XX, Z
containing NaN, NA, Inf
are
discarded with non-fatal warnings
Upon execution, MCMC reports are made every 1,000 rounds to indicate progress
Stationary (non-treed) processes on larger inputs (e.g., X,Z
) of
size greater than 500, *might* be slow in execution, especially on older
machines. Once the C code starts executing, it can be interrupted in
the usual way: either via Ctrl-C (Unix-alikes) or pressing the Stop
button in the R-GUI. When this happens, interrupt messages will
indicate which required cleanup measures completed before returning
control to R
Regarding traces=TRUE
: Samples from the posterior will be
collected for all parameters in the model, except those of the
hierarchical priors, e.g., b0
, etc. Traces for some parameters
are stored in memory, others in files. GP parameters are collected
with reference to the locations in XX
, resulting
nn=dim{XX}[2]
traces of d,g,s2,tau2
, etc. Therefore, it
is recommended that nn
is chosen to be a small, representative,
set of input locations. Besides GP parameters, traces are saved for
the tree partitions, areas under the LLM, log posterior (as a function
of tree height), and samples ZZ
from the posterior predictive
distribution at XX
Robert B. Gramacy rbgramacy@ams.ucsc.edu
Gramacy, R. B., Lee, H. K. H. (2006). Bayesian treed Gaussian process models. Available as UCSC Technical Report ams2006-01.
Gramacy, R. B., Lee, H. K. H. (2006). Adaptive design of supercomputer experiments. Available as UCSC Technical Report ams2006-02.
Gramacy, R. B., Lee, H. K. H., & Macready, W. (2004). Parameter space exploration with Gaussian process trees. ICML (pp. 353–360). Omnipress & ACM Digital Library.
Chipman, H., George, E., & McCulloch, R. (1998). Bayesian CART model search (with discussion). Journal of the American Statistical Association, 93, 935–960.
Chipman, H., George, E., & McCulloch, R. (2002). Bayesian treed models. Machine Learning, 48, 303–324.
http://www.ams.ucsc.edu/~rbgramacy/tgp.html
tgp.default.params
, bgpllm
, btlm
,
blm
, bgp
, btgpllm
bgp
,
plot.tgp
, tgp.trees
## ## Many of the examples below illustrate the above ## function(s) on random data. Thus it can be fun ## (and informative) to run them several times. ## # # simple linear response # # input and predictive data X <- seq(0,1,length=50) XX <- seq(0,1,length=99) Z <- 1 + 2*X + rnorm(length(X),sd=0.25) # out <- blm(X=X, Z=Z, XX=XX) # try Linear Model with tgp p <- tgp.default.params(2) p$tree <- c(0,0,10) # no tree p$gamma <- c(-1,0.2,0.7) # force llm out <- tgp(X=X,Z=Z,XX=XX,params=p) plot(out) # plot the surface # # 1-d Example # # construct some 1-d nonstationary data X <- seq(0,20,length=100) XX <- seq(0,20,length=99) Z <- (sin(pi*X/5) + 0.2*cos(4*pi*X/5)) * (X <= 9.6) lin <- X>9.6; Z[lin] <- -1 + X[lin]/10 Z <- Z + rnorm(length(Z), sd=0.1) # out <- btlm(X=X, Z=Z, XX=XX) # try Linear CART with tgp p <- tgp.default.params(2) p$gamma <- c(-1,0.2,0.7) # force llm out <- tgp(X=X,Z=Z,XX=XX,params=p) plot(out) # plot the surface tgp.trees(out) # plot the MAP trees # out <- btgp(X=X, Z=Z, XX=XX) # use a treed GP with tgp p <- tgp.default.params(2) p$gamma <- c(0,0.2,0.7) # force no llm out <- tgp(X=X,Z=Z,XX=XX,params=p) plot(out) # plot the surface tgp.trees(out) # plot the MAP trees # # 2-d example # (using the isotropic correlation function) # # construct some 2-d nonstationary data exp2d.data <- exp2d.rand() X <- exp2d.data$X; Z <- exp2d.data$Z XX <- exp2d.data$XX # try a GP with tgp # out <- bgp(X=X, Z=Z, XX=XX, corr="exp") p <- tgp.default.params(3) p$tree <- c(0,0,10) # no tree p$gamma <- c(0,0.2,0.7) # no llm p$corr <- "exp" out <- tgp(X=X,Z=Z,XX=XX,params=p) plot(out) # plot the surface # try a treed GP LLM with tgp # out <- btgpllm(X=X,Z=Z,XX=XX,corr="exp") p <- tgp.default.params(3) p$corr <- "exp" out <- tgp(X=X,Z=Z,XX=XX,params=p) plot(out) # plot the surface tgp.trees(out) # plot the MAP trees # # Motorcycle Accident Data # # get the data require(MASS) # try a custom treed GP LLM with tgp, without m0r1 p <- tgp.default.params(2) p$bprior <- "b0" # beta linear prior for common mean p$nug.p <- c(1.0,0.1,10.0,0.1) # mixture nugget prior out <- tgp(X=mcycle[,1], Z=mcycle[,2], params=p, BTE=c(2000,22000,2)) # run mcmc longer plot(out) # plot the surface tgp.trees(out) # plot the MAP trees # for other examples try the demos or the vignette