gbm: Generalized Boosted Regression Modeling

In gbm-developers/gbm3: Generalized Boosted Regression Models

Generalized Boosted Regression Modeling

Description

Fits generalized boosted regression models.

Usage

gbm.fit(
  x,
  y,
  offset = NULL,
  distribution = "bernoulli",
  w = NULL,
  var.monotone = NULL,
  n.trees = 100,
  interaction.depth = 1,
  n.minobsinnode = 10,
  shrinkage = 0.001,
  bag.fraction = 0.5,
  nTrain = NULL,
  train.fraction = NULL,
  mFeatures = NULL,
  keep.data = TRUE,
  verbose = TRUE,
  var.names = NULL,
  response.name = "y",
  group = NULL,
  tied.times.method = "efron",
  prior.node.coeff.var = 1000,
  strata = NA,
  obs.id = 1:nrow(x)
)

gbm(
  formula = formula(data),
  distribution = "bernoulli",
  data = list(),
  weights,
  subset = NULL,
  offset = NULL,
  var.monotone = NULL,
  n.trees = 100,
  interaction.depth = 1,
  n.minobsinnode = 10,
  shrinkage = 0.001,
  bag.fraction = 0.5,
  train.fraction = 1,
  mFeatures = NULL,
  cv.folds = 0,
  keep.data = TRUE,
  verbose = FALSE,
  class.stratify.cv = NULL,
  n.cores = NULL,
  par.details = getOption("gbm.parallel"),
  fold.id = NULL,
  tied.times.method = "efron",
  prior.node.coeff.var = 1000,
  strata = NA,
  obs.id = 1:nrow(data)
)

Arguments

x, y	For gbm.fit: x is a data frame or data matrix containing the predictor variables and y is a matrix of outcomes. Excluding coxph this matrix of outcomes collapses to a vector, in the case of coxph it is a survival object where the event times fill the first one (or two columns) and the status fills the final column. The number of rows in x must be the same as the length of the 1st dimension of y.
offset	an optional model offset
distribution	either a character string specifying the name of the distribution to use or a list with a component name specifying the distribution and any additional parameters needed. If not specified, gbm will try to guess: if the response has only two unique values, bernoulli is assumed (two-factor responses are converted to 0,1); otherwise, if the response has class "Surv", coxph is assumed; otherwise, gaussian is assumed. Available distributions are "gaussian" (squared error), "laplace" (absolute loss), "tdist" (t-distribution loss), "bernoulli" (logistic regression for 0-1 outcomes), "huberized" (Huberized hinge loss for 0-1 outcomes), "adaboost" (the AdaBoost exponential loss for 0-1 outcomes), "poisson" (count outcomes), "coxph" (right censored observations), "quantile", or "pairwise" (ranking measure using the LambdaMART algorithm). If quantile regression is specified, distribution must be a list of the form list(name="quantile",alpha=0.25) where alpha is the quantile to estimate. Non-constant weights are unsupported. If "tdist" is specified, the default degrees of freedom is four and this can be controlled by specifying distribution=list(name="tdist", df=DF) where DF is your chosen degrees of freedom. If "pairwise" regression is specified, distribution must be a list of the form list(name="pairwise",group=...,metric=...,max.rank=...) (metric and max.rank are optional, see below). group is a character vector with the column names of data that jointly indicate the group an instance belongs to (typically a query in Information Retrieval applications). For training, only pairs of instances from the same group and with different target labels can be considered. metric is the IR measure to use, one of list("conc") Fraction of concordant pairs; for binary labels, this is equivalent to the Area under the ROC Curve : Fraction of concordant pairs; for binary labels, this is equivalent to the Area under the ROC Curve list("mrr") Mean reciprocal rank of the highest-ranked positive instance : Mean reciprocal rank of the highest-ranked positive instance list("map") Mean average precision, a generalization of mrr to multiple positive instances : Mean average precision, a generalization of mrr to multiple positive instances list("ndcg:") Normalized discounted cumulative gain. The score is the weighted sum (DCG) of the user-supplied target values, weighted by log(rank+1), and normalized to the maximum achievable value. This is the default if the user did not specify a metric. ndcg and conc allow arbitrary target values, while binary targets {0,1} are expected for map and mrr. For ndcg and mrr, a cut-off can be chosen using a positive integer parameter max.rank. If left unspecified, all ranks are taken into account. Note that splitting of instances into training and validation sets follows group boundaries and therefore only approximates the specified train.fraction ratio (the same applies to cross-validation folds). Internally queries are randomly shuffled before training to avoid bias. Weights can be used in conjunction with pairwise metrics, however it is assumed that they are constant for instances from the same group. For details and background on the algorithm, see e.g. Burges (2010).
w	For gbm.fit: w is a vector of weights of the same length as the 1st dimension of y.
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.
interaction.depth	The maximum depth of variable interactions: 1 builds an additive model, 2 builds a model with up to two-way interactions, etc.
n.minobsinnode	minimum number of observations (not total weights) in the terminal nodes of the trees.
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 independent training observations (or patients) randomly selected to propose the next tree in the expansion, depending on the obs.id vector multiple training data rows may belong to a single 'patient'. This introduces randomness into the model fit. If bag.fraction<1 then running the same model twice will result in similar but different fits. gbm uses the R random number generator, so set.seed ensures the same model can be reconstructed. Preferably, the user can save the returned GBMFit object using save.
nTrain	An integer representing the number of unique patients, each patient could have multiple rows associated with them, on which to train. This is the preferred way of specification for gbm.fit; The option train.fraction in gbm.fit is deprecated and only maintained for backward compatibility. These two parameters are mutually exclusive. If both are unspecified, all data is used for training.
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.
mFeatures	Each node will be trained on a random subset of mFeatures number of features. Each node will consider a new random subset of features, adding variability to tree growth and reducing computation time. mFeatures will be bounded between 1 and nCols. Values outside of this bound will be set to the lower or upper limits.
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 extra copy of the dataset.
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.
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.
group	group used when distribution = 'pairwise'.
tied.times.method	For gbm and gbm.fit: This is an optional string used with CoxPH distribution specifying what method to employ when dealing with tied times. Currently only "efron" and "breslow" are available; the default value is "efron". Setting the string to any other value reverts the method to the original CoxPH model implementation where ties are not explicitly dealt with.
prior.node.coeff.var	Optional double only used with the coxph distribution. It is a prior on the coefficient of variation associated with the hazard rate assigned to each terminal node when fitting a tree.Increasing its value emphasises the importance of the training data in the node when assigning a prediction to said node.
strata	Optional vector of integers (or factors) only used with the coxph distributions. Each integer in this vector represents the stratum the corresponding row in the data belongs to, e. g. if the 10th element is 3 then the 10th data row belongs to the 3rd strata.
obs.id	Optional vector of integers used to specify which rows of data belong to individual patients. Data is then bagged by patient id; the default sets each row of the data to belong to an individual patient.
formula	a symbolic description of the model to be fit. The formula may include an offset term (e.g. y~offset(n)+x). If keep.data=FALSE in the initial call to gbm then it is the user's responsibility to resupply the offset to gbm_more.
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 to gbm then gbm stores a copy with the object. If keep.data=FALSE then subsequent calls to gbm_more must resupply the same dataset. It becomes the user's responsibility to resupply the same data at this point.
weights	an optional vector of weights to be used in the fitting process. The weights 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 gbm_more.
subset	an optional vector defining a subset of the data to be used
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 and calculate an estimate of generalization error returned in cv_error.
class.stratify.cv	whether the cross-validation should be stratified by class. Is only implemented for bernoulli. The purpose of stratifying the cross-validation is to help avoiding situations in which training sets do not contain all classes.
n.cores	number of cores to use for parallelization. Please use par.details instead; this argument is only provided for convenience.
par.details	Details of the parallelization to use in the core algorithm.
fold.id	An optional vector of values identifying what fold each observation is in. If supplied, cv.folds can be missing. Note: Multiple observations to the same patient must have the same fold id.

Details

See the gbm vignette for technical 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 GBMFit 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 is a deprecated function that now acts as a front-end to gbmt_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 over gbm; however gbmt and gbmt_fit are now the current APIs.

Value

gbm and gbm.fit return a GBMFit object.

Functions

• gbm.fit(): Core fitting code, for experts only.

Author(s)

James Hickey, Greg Ridgeway [e-mail]

Quantile regression code developed by Brian Kriegler [e-mail]

t-distribution code developed by Harry Southworth and Daniel Edwards

Pairwise code developed by Stefan Schroedl [e-mail]

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.

B. Kriegler (2007). Cost-Sensitive Stochastic Gradient Boosting Within a Quantitative Regression Framework. PhD dissertation, UCLA Statistics.

C. Burges (2010). “From RankNet to LambdaRank to LambdaMART: An Overview,” Microsoft Research Technical Report MSR-TR-2010-82.

Greg Ridgeway's site.

The MART website.

See Also

gbmt, gbmt_fit gbmt_performance, plot, predict.GBMFit, summary.GBMFit, pretty_gbm_tree, gbmParallel.

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",     # see the help for other choices
    n.trees=1000,                # number of trees
    shrinkage=0.05,              # 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
    mFeatures = 3,               # half of the features are considered at each node
    n.minobsinnode = 10,         # minimum total weight needed in each node
    cv.folds = 3,                # do 3-fold cross-validation
    keep.data=TRUE,              # keep a copy of the dataset with the object
    verbose=FALSE                # don't print out progress
# , par.details=gbmParallel(num_threads=15) # option for gbm3 to parallelize
    )                   

# check performance using an out-of-bag estimator
# OOB underestimates the optimal number of iterations
best_iter <- gbmt_performance(gbm1,method="OOB")
print(best_iter)

# check performance using a 50% heldout test set
best_iter <- gbmt_performance(gbm1,method="test")
print(best_iter)

# check performance using 3-fold cross-validation
best_iter <- gbmt_performance(gbm1,method="cv")
print(best_iter)

# plot the performance # plot variable influence
summary(gbm1, num_trees=1)         # based on the first tree
summary(gbm1, num_trees=best_iter) # based on the estimated best number of trees

# compactly print the first and last trees for curiosity
print(pretty_gbm_tree(gbm1,1))
print(pretty_gbm_tree(gbm1,gbm1$params$num_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(gbm1,data2,best_iter)

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

# create marginal plots
# plot variable X1,X2,X3 after "best" iterations
oldpar <- par(no.readonly = TRUE)
par(mfrow=c(1,3))
plot(gbm1,1,best_iter)
plot(gbm1,2,best_iter)
plot(gbm1,3,best_iter)
par(mfrow=c(1,1))
# contour plot of variables 1 and 2 after "best" iterations
plot(gbm1,1:2,best_iter)
# lattice plot of variables 2 and 3
plot(gbm1,2:3,best_iter)
# lattice plot of variables 3 and 4
plot(gbm1,3:4,best_iter)

# 3-way plots
plot(gbm1,c(1,2,6),best_iter,cont=20)
plot(gbm1,1:3,best_iter)
plot(gbm1,2:4,best_iter)
plot(gbm1,3:5,best_iter)
par(oldpar) # reset graphics options to previous settings

# do another 100 iterations
gbm2 <- gbm_more(gbm1,100,
                 is_verbose=FALSE) # stop printing detailed progress

gbm-developers/gbm3 documentation built on April 28, 2024, 10:04 p.m.