bark {bark}  R Documentation 
Nonparametric Regression using Bayesian Additive Regression Kernels
Description
BARK is a Bayesian sumofkernels 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 Gaussian kernel functions.
The goal is to have very flexible inference for the unknown
function f
.
BARK uses an approximation to a Cauchy process as the prior distribution
for the unknown function f
.
Feature selection can be achieved through the inference on the scale parameters in the Gaussian kernels. BARK accepts four different types of prior distributions, e, d, enabling either soft shrinkage or se, sd, enabling hard shrinkage for the scale parameters.
Usage
bark(
formula,
data,
subset,
na.action = na.omit,
testdata = NULL,
selection = TRUE,
common_lambdas = TRUE,
classification = FALSE,
keepevery = 100,
nburn = 100,
nkeep = 100,
printevery = 1000,
keeptrain = FALSE,
verbose = FALSE,
fixed = list(),
tune = list(lstep = 0.5, frequL = 0.2, dpow = 1, upow = 0, varphistep = 0.5, phistep =
1),
theta = list()
)
Arguments
formula 
model formula for the model with all predictors, Y ~ X. The X variables will be centered and scaled as part of model fitting. 
data 
a data frame. Factors will be converted to numerical vectors based on the using 'model.matrix'. 
subset 
an optional vector specifying a subset of observations to be used in the fitting process. 
na.action 
a function which indicates what should happen when the data contain NAs. The default is "na.omit". 
testdata 
Dataframe with test data for out of sample prediction. 
selection 
Logical variable indicating whether variable
dependent kernel parameters 
common_lambdas 
Logical variable indicating whether
kernel parameters 
classification 
TRUE/FALSE logical variable, indicating a classification or regression problem. 
keepevery 
Every keepevery draw is kept to be returned to the user 
nburn 
Number of MCMC iterations (nburn*keepevery) to be treated as burn in. 
nkeep 
Number of MCMC iterations kept for the posterior inference. 
printevery 
As the MCMC runs, a message is printed every printevery draws. 
keeptrain 
Logical, whether to keep results for training samples. 
verbose 
Logical, whether to print out messages 
fixed 
A list of fixed hyperparameters, using the default values if not
specified. 
tune 
A list of tuning parameters, not expected to change. 
theta 
A list of the starting values for the parameter theta, use defaults if nothing is given. 
Details
BARK is implemented using a Bayesian MCMC method. At each MCMC interaction, we produce a draw from the joint posterior distribution, i.e. a full configuration of regression coefficients, kernel locations and kernel parameters.
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)
Value
bark
returns an object of class 'bark' with a list, including:
call 
the matched call 
fixed 
Fixed hyperparameters 
tune 
Tuning parameters used 
theta.last 
The last set of parameters from the posterior draw 
theta.nvec 
A matrix with nrow(x.train) 
theta.varphi 
A matrix with nrow(x.train)

theta.beta 
A matrix with nrow(x.train) 
theta.lambda 
A matrix with ncol(x.train) rows and (nkeep) columns, recording the kernel scale parameters 
thea.phi 
The vector of length nkeep, recording the precision in regression Gaussian noise (1 for the classification case) 
yhat.train 
A matrix with nrow(x.train) rows and (nkeep) columns.
Each column corresponds to a draw 
yhat.test 
Same as yhat.train but now the x's are the rows of the test data; NULL if testdata are not provided 
yhat.train.mean 
train data fits = row mean of yhat.train 
yhat.test.mean 
test data fits = row mean of yhat.test 
References
Ouyang, Zhi (2008) Bayesian Additive Regression Kernels. Duke University. PhD dissertation, page 58.
See Also
Other bark functions:
barkpackagedeprecated
,
barkpackage
,
sim_Friedman1()
,
sim_Friedman2()
,
sim_Friedman3()
,
sim_circle()
Examples
##Simulated regression example
# Friedman 2 data set, 200 noisy training, 1000 noise free testing
# Out of sample MSE in SVM (default RBF): 6500 (sd. 1600)
# Out of sample MSE in BART (default): 5300 (sd. 1000)
traindata < data.frame(sim_Friedman2(200, sd=125))
testdata < data.frame(sim_Friedman2(1000, sd=0))
# example with a very small number of iterations to illustrate usage
fit.bark.d < bark(y ~ ., data=traindata, testdata= testdata,
nburn=10, nkeep=10, keepevery=10,
classification=FALSE,
common_lambdas = FALSE,
selection = FALSE)
boxplot(data.frame(fit.bark.d$theta.lambda))
mean((fit.bark.d$yhat.test.meantestdata$y)^2)
##Simulate classification example
# Circle 5 with 2 signals and three noisy dimensions
# Out of sample erorr rate in SVM (default RBF): 0.110 (sd. 0.02)
# Out of sample error rate in BART (default): 0.065 (sd. 0.02)
traindata < sim_circle(200, dim=5)
testdata < sim_circle(1000, dim=5)
fit.bark.se < bark(y ~ .,
data=data.frame(traindata),
testdata= data.frame(testdata),
classification=TRUE,
nburn=100, nkeep=200, )
boxplot(as.data.frame(fit.bark.se$theta.lambda))
mean((fit.bark.se$yhat.test.mean>0)!=testdata$y)