rs.pbart: BART for dichotomous outcomes with parallel computation and...
In BART: Bayesian Additive Regression Trees
rs.pbart R Documentation
BART for dichotomous outcomes with parallel computation and
stratified random sampling
Description
BART is a Bayesian “sum-of-trees” model.
For numeric response y, we have
y = f(x) + \epsilon,
where \epsilon \sim N(0,\sigma^2).
For a binary response y, P(Y=1 | x) = F(f(x)), where F
denotes the standard normal cdf (probit link).
In both cases, f is the sum of many tree models.
The goal is to have very flexible inference for the uknown
function f.
In the spirit of “ensemble models”,
each tree is constrained by a prior to be a weak learner
so that it contributes a
small amount to the overall fit.
Usage
rs.pbart(
x.train, y.train, x.test=matrix(0.0,0,0),
C=floor(length(y.train)/2000),
k=2.0, power=2.0, base=.95,
binaryOffset=0,
ntree=50L, numcut=100L,
ndpost=1000L, nskip=100L,
keepevery=1L, printevery=100,
keeptrainfits=FALSE, transposed=FALSE,
mc.cores = 2L, nice = 19L,
seed = 99L
)
Arguments
x.train
Explanatory variables for training (in sample) data.
May be a matrix or a data frame,
with (as usual) rows corresponding to observations and columns to variables.
If a variable is a factor in a data frame, it is replaced with dummies.
Note that q dummies are created if q>2 and
one dummy is created if q=2, where q is the number of levels of the factor.
pbart will generate draws of f(x) for each x
which is a row of x.train.
y.train
Dependent variable for training (in sample) data.
If y is numeric a continous response model is fit (normal errors).
If y is a factor (or just has values 0 and 1) then a binary response model
with a probit link is fit.
x.test
Explanatory variables for test (out of sample) data.
Should have same structure as x.train.
pbart will generate draws of f(x) for each x which is a row of x.test.
C
The number of shards to break the data into and analyze separately.
k
For binary y,
k is the number of prior standard deviations f(x) is away from +/-3.
In both cases, the bigger k is, the more conservative the fitting will be.
power
Power parameter for tree prior.
base
Base parameter for tree prior.
binaryOffset
Used for binary y.
The model is P(Y=1 | x) = F(f(x) + binaryOffset).
The idea is that f is shrunk towards 0, so the offset allows you to shrink towards
a probability other than .5.
ntree
The number of trees in the sum.
numcut
The number of possible values of c (see usequants).
If a single number if given, this is used for all variables.
Otherwise a vector with length equal to ncol(x.train) is required,
where the i^{th} element gives the number of c used for
the i^{th} variable in x.train.
If usequants is false, numcut equally spaced cutoffs
are used covering the range of values in the corresponding
column of x.train. If usequants is true, then min(numcut, the number of unique values in the
corresponding columns of x.train - 1) c values are used.
ndpost
The number of posterior draws returned.
nskip
Number of MCMC iterations to be treated as burn in.
keepevery
Every keepevery draw is kept to be returned to the user.
printevery
As the MCMC runs, a message is printed every printevery draws.
keeptrainfits
Whether to keep yhat.train or not.
transposed
When running pbart in parallel, it is more memory-efficient
to transpose x.train and x.test, if any, prior to
calling mc.pbart.
seed
Setting the seed required for reproducible MCMC.
mc.cores
Number of cores to employ in parallel.
nice
Set the job niceness. The default
niceness is 19: niceness goes from 0 (highest) to 19 (lowest).
Details
BART is an Bayesian MCMC method.
At each MCMC interation, we produce a draw from the joint posterior
(f,\sigma) | (x,y) in the numeric y case
and just f in the binary y case.
Thus, unlike a lot of other modelling methods in R, we do not produce a single model object
from which fits and summaries may be extracted. The output consists of values
f^*(x) (and \sigma^* in the numeric case) where * denotes a particular draw.
The x is either a row from the training data (x.train) or the test data (x.test).
Value
rs.pbart returns an object of type pbart which is
essentially a list.
yhat.shard
Estimates generated from the individual shards rather than from the
whole. This object is only useful for assessing convergence.
A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw f^* from the posterior of f
and each column corresponds to a row of x.train.
The (i,j) value is f^*(x) for the i^{th} kept draw of f
and the j^{th} row of x.train.
Burn-in is dropped.
yhat.train
Estimates generated from the whole if keeptrainfits=TRUE.
A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw f^* from the posterior of f
and each column corresponds to a row of x.train.
The (i,j) value is f^*(x) for the i^{th} kept draw of f
and the j^{th} row of x.train.
Burn-in is dropped.
yhat.test
Estimates generated from the whole if x.test is provided.
Same as yhat.train but now the x's are the rows of the test data.
varcount
a matrix with ndpost rows and nrow(x.train) columns.
Each row is for a draw. For each variable (corresponding to the columns),
the total count of the number of times
that variable is used in a tree decision rule (over all trees) is given.
In addition the list
has a binaryOffset component giving the value used.
Note that in the binary y, case yhat.train and yhat.test are
f(x) + binaryOffset. If you want draws of the probability
P(Y=1 | x) you need to apply the normal cdf (pnorm)
to these values.
See Also
mc.pbart
Examples
##simulate from Friedman's five-dimensional test function
##Friedman JH. Multivariate adaptive regression splines
##(with discussion and a rejoinder by the author).
##Annals of Statistics 1991; 19:1-67.
f = function(x) #only the first 5 matter
sin(pi*x[ , 1]*x[ , 2]) + 2*(x[ , 3]-.5)^2+x[ , 4]+0.5*x[ , 5]-1.5
sigma = 1.0 #y = f(x) + sigma*z where z~N(0, 1)
k = 50 #number of covariates
thin = 25
ndpost = 2500
nskip = 100
C = 10
m = 10
n = 10000
set.seed(12)
x.train=matrix(runif(n*k), n, k)
Ey.train = f(x.train)
y.train=(Ey.train+sigma*rnorm(n)>0)*1
table(y.train)/n
x <- x.train
x4 <- seq(0, 1, length.out=m)
for(i in 1:m) {
x[ , 4] <- x4[i]
if(i==1) x.test <- x
else x.test <- rbind(x.test, x)
}
## parallel::mcparallel/mccollect do not exist on windows
if(.Platform$OS.type=='unix') {
##test BART with token run to ensure installation works
post = rs.pbart(x.train, y.train,
C=C, mc.cores=4, keepevery=1,
seed=99, ndpost=1, nskip=1)
}
## Not run:
post = rs.pbart(x.train, y.train, x.test=x.test,
C=C, mc.cores=8, keepevery=thin,
seed=99, ndpost=ndpost, nskip=nskip)
str(post)
par(mfrow=c(2, 2))
M <- nrow(post$yhat.test)
pred <- matrix(nrow=M, ncol=10)
for(i in 1:m) {
h <- (i-1)*n+1:n
pred[ , i] <- apply(pnorm(post$yhat.test[ , h]), 1, mean)
}
pred <- apply(pred, 2, mean)
plot(x4, qnorm(pred), xlab=expression(x[4]),
ylab='partial dependence function', type='l')
i <- floor(seq(1, n, length.out=10))
j <- seq(-0.5, 0.4, length.out=10)
for(h in 1:10) {
auto.corr <- acf(post$yhat.shard[ , i[h]], plot=FALSE)
if(h==1) {
max.lag <- max(auto.corr$lag[ , 1, 1])
plot(1:max.lag+j[h], auto.corr$acf[1+(1:max.lag), 1, 1],
type='h', xlim=c(0, max.lag+1), ylim=c(-1, 1),
ylab='auto-correlation', xlab='lag')
}
else
lines(1:max.lag+j[h], auto.corr$acf[1+(1:max.lag), 1, 1],
type='h', col=h)
}
for(j in 1:10) {
if(j==1)
plot(pnorm(post$yhat.shard[ , i[j]]),
type='l', ylim=c(0, 1),
sub=paste0('N:', n, ', k:', k),
ylab=expression(Phi(f(x))), xlab='m')
else
lines(pnorm(post$yhat.shard[ , i[j]]),
type='l', col=j)
}
geweke <- gewekediag(post$yhat.shard)
j <- -10^(log10(n)-1)
plot(geweke$z, pch='.', cex=2, ylab='z', xlab='i',
sub=paste0('N:', n, ', k:', k),
xlim=c(j, n), ylim=c(-5, 5))
lines(1:n, rep(-1.96, n), type='l', col=6)
lines(1:n, rep(+1.96, n), type='l', col=6)
lines(1:n, rep(-2.576, n), type='l', col=5)
lines(1:n, rep(+2.576, n), type='l', col=5)
lines(1:n, rep(-3.291, n), type='l', col=4)
lines(1:n, rep(+3.291, n), type='l', col=4)
lines(1:n, rep(-3.891, n), type='l', col=3)
lines(1:n, rep(+3.891, n), type='l', col=3)
lines(1:n, rep(-4.417, n), type='l', col=2)
lines(1:n, rep(+4.417, n), type='l', col=2)
text(c(1, 1), c(-1.96, 1.96), pos=2, cex=0.6, labels='0.95')
text(c(1, 1), c(-2.576, 2.576), pos=2, cex=0.6, labels='0.99')
text(c(1, 1), c(-3.291, 3.291), pos=2, cex=0.6, labels='0.999')
text(c(1, 1), c(-3.891, 3.891), pos=2, cex=0.6, labels='0.9999')
text(c(1, 1), c(-4.417, 4.417), pos=2, cex=0.6, labels='0.99999')
par(mfrow=c(1, 1))
##dev.copy2pdf(file='geweke.rs.pbart.pdf')
## End(Not run)
BART documentation built on June 22, 2024, 11:33 a.m.
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| rs.pbart | R Documentation |
BART for dichotomous outcomes with parallel computation and stratified random sampling
Description
BART is a Bayesian “sum-of-trees” model.
For numeric response y, we have
y = f(x) + \epsilon,
where \epsilon \sim N(0,\sigma^2).
For a binary response y, P(Y=1 | x) = F(f(x)), where F
denotes the standard normal cdf (probit link).
In both cases, f is the sum of many tree models.
The goal is to have very flexible inference for the uknown
function f.
In the spirit of “ensemble models”, each tree is constrained by a prior to be a weak learner so that it contributes a small amount to the overall fit.
Usage
rs.pbart(
x.train, y.train, x.test=matrix(0.0,0,0),
C=floor(length(y.train)/2000),
k=2.0, power=2.0, base=.95,
binaryOffset=0,
ntree=50L, numcut=100L,
ndpost=1000L, nskip=100L,
keepevery=1L, printevery=100,
keeptrainfits=FALSE, transposed=FALSE,
mc.cores = 2L, nice = 19L,
seed = 99L
)
Arguments
x.train |
Explanatory variables for training (in sample) data. |
y.train |
Dependent variable for training (in sample) data. |
x.test |
Explanatory variables for test (out of sample) data. |
C |
The number of shards to break the data into and analyze separately. |
k |
For binary y,
k is the number of prior standard deviations |
power |
Power parameter for tree prior. |
base |
Base parameter for tree prior. |
binaryOffset |
Used for binary |
ntree |
The number of trees in the sum. |
numcut |
The number of possible values of c (see usequants).
If a single number if given, this is used for all variables.
Otherwise a vector with length equal to ncol(x.train) is required,
where the |
ndpost |
The number of posterior draws returned. |
nskip |
Number of MCMC iterations to be treated as burn in. |
keepevery |
Every keepevery draw is kept to be returned to the user. |
printevery |
As the MCMC runs, a message is printed every printevery draws. |
keeptrainfits |
Whether to keep |
transposed |
When running |
seed |
Setting the seed required for reproducible MCMC. |
mc.cores |
Number of cores to employ in parallel. |
nice |
Set the job niceness. The default niceness is 19: niceness goes from 0 (highest) to 19 (lowest). |
Details
BART is an Bayesian MCMC method.
At each MCMC interation, we produce a draw from the joint posterior
(f,\sigma) | (x,y) in the numeric y case
and just f in the binary y case.
Thus, unlike a lot of other modelling methods in R, we do not produce a single model object
from which fits and summaries may be extracted. The output consists of values
f^*(x) (and \sigma^* in the numeric case) where * denotes a particular draw.
The x is either a row from the training data (x.train) or the test data (x.test).
Value
rs.pbart returns an object of type pbart which is
essentially a list.
yhat.shard |
Estimates generated from the individual shards rather than from the whole. This object is only useful for assessing convergence. A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw |
yhat.train |
Estimates generated from the whole if A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw |
yhat.test |
Estimates generated from the whole if Same as yhat.train but now the x's are the rows of the test data. |
varcount |
a matrix with ndpost rows and nrow(x.train) columns. Each row is for a draw. For each variable (corresponding to the columns), the total count of the number of times that variable is used in a tree decision rule (over all trees) is given. |
In addition the list has a binaryOffset component giving the value used.
Note that in the binary y, case yhat.train and yhat.test are
f(x) + binaryOffset. If you want draws of the probability
P(Y=1 | x) you need to apply the normal cdf (pnorm)
to these values.
See Also
mc.pbart
Examples
##simulate from Friedman's five-dimensional test function
##Friedman JH. Multivariate adaptive regression splines
##(with discussion and a rejoinder by the author).
##Annals of Statistics 1991; 19:1-67.
f = function(x) #only the first 5 matter
sin(pi*x[ , 1]*x[ , 2]) + 2*(x[ , 3]-.5)^2+x[ , 4]+0.5*x[ , 5]-1.5
sigma = 1.0 #y = f(x) + sigma*z where z~N(0, 1)
k = 50 #number of covariates
thin = 25
ndpost = 2500
nskip = 100
C = 10
m = 10
n = 10000
set.seed(12)
x.train=matrix(runif(n*k), n, k)
Ey.train = f(x.train)
y.train=(Ey.train+sigma*rnorm(n)>0)*1
table(y.train)/n
x <- x.train
x4 <- seq(0, 1, length.out=m)
for(i in 1:m) {
x[ , 4] <- x4[i]
if(i==1) x.test <- x
else x.test <- rbind(x.test, x)
}
## parallel::mcparallel/mccollect do not exist on windows
if(.Platform$OS.type=='unix') {
##test BART with token run to ensure installation works
post = rs.pbart(x.train, y.train,
C=C, mc.cores=4, keepevery=1,
seed=99, ndpost=1, nskip=1)
}
## Not run:
post = rs.pbart(x.train, y.train, x.test=x.test,
C=C, mc.cores=8, keepevery=thin,
seed=99, ndpost=ndpost, nskip=nskip)
str(post)
par(mfrow=c(2, 2))
M <- nrow(post$yhat.test)
pred <- matrix(nrow=M, ncol=10)
for(i in 1:m) {
h <- (i-1)*n+1:n
pred[ , i] <- apply(pnorm(post$yhat.test[ , h]), 1, mean)
}
pred <- apply(pred, 2, mean)
plot(x4, qnorm(pred), xlab=expression(x[4]),
ylab='partial dependence function', type='l')
i <- floor(seq(1, n, length.out=10))
j <- seq(-0.5, 0.4, length.out=10)
for(h in 1:10) {
auto.corr <- acf(post$yhat.shard[ , i[h]], plot=FALSE)
if(h==1) {
max.lag <- max(auto.corr$lag[ , 1, 1])
plot(1:max.lag+j[h], auto.corr$acf[1+(1:max.lag), 1, 1],
type='h', xlim=c(0, max.lag+1), ylim=c(-1, 1),
ylab='auto-correlation', xlab='lag')
}
else
lines(1:max.lag+j[h], auto.corr$acf[1+(1:max.lag), 1, 1],
type='h', col=h)
}
for(j in 1:10) {
if(j==1)
plot(pnorm(post$yhat.shard[ , i[j]]),
type='l', ylim=c(0, 1),
sub=paste0('N:', n, ', k:', k),
ylab=expression(Phi(f(x))), xlab='m')
else
lines(pnorm(post$yhat.shard[ , i[j]]),
type='l', col=j)
}
geweke <- gewekediag(post$yhat.shard)
j <- -10^(log10(n)-1)
plot(geweke$z, pch='.', cex=2, ylab='z', xlab='i',
sub=paste0('N:', n, ', k:', k),
xlim=c(j, n), ylim=c(-5, 5))
lines(1:n, rep(-1.96, n), type='l', col=6)
lines(1:n, rep(+1.96, n), type='l', col=6)
lines(1:n, rep(-2.576, n), type='l', col=5)
lines(1:n, rep(+2.576, n), type='l', col=5)
lines(1:n, rep(-3.291, n), type='l', col=4)
lines(1:n, rep(+3.291, n), type='l', col=4)
lines(1:n, rep(-3.891, n), type='l', col=3)
lines(1:n, rep(+3.891, n), type='l', col=3)
lines(1:n, rep(-4.417, n), type='l', col=2)
lines(1:n, rep(+4.417, n), type='l', col=2)
text(c(1, 1), c(-1.96, 1.96), pos=2, cex=0.6, labels='0.95')
text(c(1, 1), c(-2.576, 2.576), pos=2, cex=0.6, labels='0.99')
text(c(1, 1), c(-3.291, 3.291), pos=2, cex=0.6, labels='0.999')
text(c(1, 1), c(-3.891, 3.891), pos=2, cex=0.6, labels='0.9999')
text(c(1, 1), c(-4.417, 4.417), pos=2, cex=0.6, labels='0.99999')
par(mfrow=c(1, 1))
##dev.copy2pdf(file='geweke.rs.pbart.pdf')
## End(Not run)
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