gbm (version 1.3-5)

gbm: Generalized Boosted Regression Modeling

Description

Fits generalized boosted regression models.

Usage

gbm(formula = formula(data),
    distribution = "bernoulli",
    data = list(),
    weights,
    offset = NULL,
    var.monotone = NULL,
    n.trees = 100,
    interaction.depth = 1,
    n.minobsinnode = 10,
    shrinkage = 0.001,
    bag.fraction = 0.5,
    train.fraction = 1.0,
    cv.folds=0,
    keep.data = TRUE,
    verbose = TRUE)

gbm.fit(x,y,
        offset = NULL,
        misc = NULL,
        distribution = "bernoulli",
        w = NULL,
        var.monotone = NULL,
        n.trees = 100,
        interaction.depth = 1,
        n.minobsinnode = 10,
        shrinkage = 0.001,
        bag.fraction = 0.5,
        train.fraction = 1.0,
        keep.data = TRUE,
        verbose = TRUE,
        var.names = NULL,
        response.name = NULL)

gbm.more(object,
         n.new.trees = 100,
         data = NULL,
         weights = NULL,
         offset = NULL,
         verbose = NULL)

Arguments

formula

a symbolic description of the model to be fit.

distribution

a description of the error distribution to be used in the model. Currently available options are "gaussian" (squared error), "laplace" (absolute loss), "bernoulli" (logistic regression for 0-1 outcomes), "adaboost" (the AdaBoost exponential loss for 0-

data

an optional data frame containing the variables in the model. By default the variables are taken from environment(formula), typically the environment from which gbm is called. If keep.data=TRUE in the initial call

weights

an optional vector of weights to be used in the fitting process. Must be positive but do not need to be normalized. If keep.data=FALSE in the initial call to gbm then it is the user's responsibility to resupply the weights to

offset

an optional offset term to be used in the fitting process. Offsets cannot be expressed as part of formula. If keep.data=FALSE in the initial call to gbm then it is the user's responsibility to resupply the offset

var.monotone

an optional vector, the same length as the number of predictors, indicating which variables have a monotone increasing (+1), decreasing (-1), or arbitrary (0) relationship with the outcome.

n.trees

the total number of trees to fit. This is equivalent to the number of iterations and the number of basis functions in the additive expansion.

cv.folds

Number of cross-validation folds to perform. If cv.folds>1 then gbm, in addition to the usual fit, will perform a cross-validation, calculate an estimate of generalization error returned in cv.error.

interaction.depth

The maximum depth of variable interactions. 1 implies an additive model, 2 implies a model with up to 2-way interactions, etc.

n.minobsinnode

minimum number of observations in the trees terminal nodes. Note that this is the actual number of observations not the total weight.

shrinkage

a shrinkage parameter applied to each tree in the expansion. Also known as the learning rate or step-size reduction.

bag.fraction

the fraction of the training set observations randomly selected to propose the next tree in the expansion. This introduces randomnesses into the model fit. If bag.fraction

train.fraction

The first train.fraction * nrows(data) observations are used to fit the gbm and the remainder are used for computing out-of-sample estimates of the loss function.

keep.data

a logical variable indicating whether to keep the data and an index of the data stored with the object. Keeping the data and index makes subsequent calls to gbm.more faster at the cost of storing an ext

object

a gbm object created from an initial call to gbm.

n.new.trees

the number of additional trees to add to object.

verbose

If TRUE, gbm will print out progress and performance indicators. If this option is left unspecified for gbm.more then it uses verbose from object.

x, y

For gbm.fit: x is a data frame or data matrix containing the predictor variables and y is the vector of outcomes. The number of rows in x must be the same as the length of y.

misc

For gbm.fit: misc is an R object that is simply passed on to the gbm engine. It can be used for additional data for the specific distribution. Currently it is only used for passing the censoring indicator for the Cox proportio

w

For gbm.fit: w is a vector of weights of the same length as the y.

var.names

For gbm.fit: A vector of strings of length equal to the number of columns of x containing the names of the predictor variables.

response.name

For gbm.fit: A character string label for the response variable.

Value

• gbm, gbm.fit, and gbm.more return a gbm.object.

Details

This package implements the generalized boosted modeling framework. Boosting is the process of iteratively adding basis functions in a greedy fashion so that each additional basis function further reduces the selected loss function. This implementation closely follows Friedman's Gradient Boosting Machine (Friedman, 2001). In addition to many of the features documented in the Gradient Boosting Machine, gbm offers additional features including the out-of-bag estimator for the optimal number of iterations, the ability to store and manipulate the resulting gbm object, and a variety of other loss functions that had not previously had associated boosting algorithms, including the Cox partial likelihood for censored data, the poisson likelihood for count outcomes, and a gradient boosting implementation to minimize the AdaBoost exponential loss function. gbm.fit provides the link between R and the C++ gbm engine. gbm is a front-end to gbm.fit that uses the familiar R modeling formulas. However, model.frame is very slow if there are many predictor variables. For power-users with many variables use gbm.fit. For general practice gbm is preferable.

References

Y. Freund and R.E. Schapire (1997) "A decision-theoretic generalization of on-line learning and an application to boosting," Journal of Computer and System Sciences, 55(1):119-139. G. Ridgeway (1999). "The state of boosting," Computing Science and Statistics 31:172-181. J.H. Friedman, T. Hastie, R. Tibshirani (2000). "Additive Logistic Regression: a Statistical View of Boosting," Annals of Statistics 28(2):337-374. J.H. Friedman (2001). "Greedy Function Approximation: A Gradient Boosting Machine," Annals of Statistics 29(5):1189-1232. J.H. Friedman (2002). "Stochastic Gradient Boosting," Computational Statistics and Data Analysis 38(4):367-378. G. Ridgeway (2003). "An out-of-bag estimator for the optimal number of boosting iterations," technical report due out soon. http://www.i-pensieri.com/gregr/gbm.shtml http://www-stat.stanford.edu/~jhf/R-MART.html

See Also

gbm.object, gbm.perf, plot.gbm, predict.gbm, summary.gbm, pretty.gbm.tree.

Examples

# A least squares regression example
# create some data

N <- 1000
X1 <- runif(N)
X2 <- 2*runif(N)
X3 <- ordered(sample(letters[1:4],N,replace=TRUE),levels=letters[4:1])
X4 <- factor(sample(letters[1:6],N,replace=TRUE))
X5 <- factor(sample(letters[1:3],N,replace=TRUE))
X6 <- 3*runif(N)
mu <- c(-1,0,1,2)[as.numeric(X3)]

SNR <- 10 # signal-to-noise ratio
Y <- X1**1.5 + 2 * (X2**.5) + mu
sigma <- sqrt(var(Y)/SNR)
Y <- Y + rnorm(N,0,sigma)

# introduce some missing values
X1[sample(1:N,size=500)] <- NA
X4[sample(1:N,size=300)] <- NA

data <- data.frame(Y=Y,X1=X1,X2=X2,X3=X3,X4=X4,X5=X5,X6=X6)

# fit initial model
gbm1 <- gbm(Y~X1+X2+X3+X4+X5+X6,         # formula
    data=data,                   # dataset
    var.monotone=c(0,0,0,0,0,0), # -1: monotone decrease,
                                 # +1: monotone increase,
                                 #  0: no monotone restrictions
    distribution="gaussian",     # bernoulli, adaboost, gaussian,
                                 # poisson, and coxph available
    n.trees=100,                 # number of trees
    shrinkage=0.001,             # shrinkage or learning rate,
                                 # 0.001 to 0.1 usually work
    interaction.depth=3,         # 1: additive model, 2: two-way interactions, etc.
    bag.fraction = 0.5,          # subsampling fraction, 0.5 is probably best
    train.fraction = 0.5,        # fraction of data for training,
                                 # first train.fraction*N used for training
    n.minobsinnode = 10,         # minimum total weight needed in each node
    keep.data=TRUE,              # keep a copy of the dataset with the object
    verbose=TRUE)                # print out progress

# check performance using an out-of-bag estimator
best.iter <- gbm.perf(gbm1,method="OOB")
# do another 100 iterations
gbm2 <- gbm.more(gbm1,100,
                 verbose=FALSE) # stop printing detailed progress

# check performance again
best.iter <- gbm.perf(gbm2,method="OOB")
# iterate until a sufficient number of trees are fit
while(gbm2$n.trees - best.iter < 10)
{
    # do 100 more iterations
    gbm2 <- gbm.more(gbm2,100)           # do another 100 iterations
    best.iter <- gbm.perf(gbm2,plot.it=FALSE,method="OOB")
}

# plot the performance
# returns test set estimate of best number of trees
best.iter <- gbm.perf(gbm2,method="test")

# plot variable influence
summary(gbm2,n.trees=1)         # based on the first tree
summary(gbm2,n.trees=best.iter) # based on the estimated best number of trees

# compactly print the first and last trees for curiosity
print(pretty.gbm.tree(gbm2,1))
print(pretty.gbm.tree(gbm2,gbm1$n.trees))

# make some new data
N <- 1000
X1 <- runif(N)
X2 <- 2*runif(N)
X3 <- ordered(sample(letters[1:4],N,replace=TRUE))
X4 <- factor(sample(letters[1:6],N,replace=TRUE))
X5 <- factor(sample(letters[1:3],N,replace=TRUE))
X6 <- 3*runif(N)
mu <- c(-1,0,1,2)[as.numeric(X3)]

Y <- X1**1.5 + 2 * (X2**.5) + mu + rnorm(N,0,sigma)

data2 <- data.frame(Y=Y,X1=X1,X2=X2,X3=X3,X4=X4,X5=X5,X6=X6)

# predict on the new data using "best" number of trees
# f.predict generally will be on the canonical scale (logit,log,etc.)
f.predict <- predict.gbm(gbm2,data2,best.iter)

# least squares error
print(sum((data2$Y-f.predict)^2))

# create marginal plots
# plot variable X1,X2,X3 after "best" iterations
par(mfrow=c(1,3))
plot.gbm(gbm2,1,best.iter)
plot.gbm(gbm2,2,best.iter)
plot.gbm(gbm2,3,best.iter)
par(mfrow=c(1,1))
# contour plot of variables 1 and 2 after "best" iterations
plot.gbm(gbm2,1:2,best.iter)
# lattice plot of variables 2 and 3
plot.gbm(gbm2,2:3,best.iter)
# lattice plot of variables 3 and 4
plot.gbm(gbm2,3:4,best.iter)

# 3-way plots
plot.gbm(gbm2,c(1,2,6),best.iter,cont=20)
plot.gbm(gbm2,1:3,best.iter)
plot.gbm(gbm2,2:4,best.iter)
plot.gbm(gbm2,3:5,best.iter)