Generalized Boosted Regression Modeling (GBM)

Workhorse function providing 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.

Usage

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,
  nTrain = NULL,
  train.fraction = NULL,
  keep.data = TRUE,
  verbose = TRUE,
  var.names = NULL,
  response.name = "y",
  group = NULL
)

Arguments

x

A data frame or matrix containing the predictor variables. The number of rows in x must be the same as the length of y.

y

A vector of outcomes. The number of rows in x must be the same as the length of y.

offset

A vector of offset values.

misc

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 proportional hazards model.

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 2 unique values, bernoulli is assumed; otherwise, if the response is a factor, multinomial is assumed; otherwise, if the response has class "Surv", coxph is assumed; otherwise, gaussian is assumed.

Currently available options 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.

If "tdist" is specified, the default degrees of freedom is 4 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

A vector of weights of the same length as the 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. A value of 1 implies an additive model, a value of 2 implies a model with up to 2-way interactions, etc. Default is 1.

n.minobsinnode

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

shrinkage

The shrinkage parameter applied to each tree in the expansion. Also known as the learning rate or step-size reduction; 0.001 to 0.1 usually work, but a smaller learning rate typically requires more trees. Default is 0.1.

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 < 1 then running the same model twice will result in similar but different fits. gbm uses the R random number generator so set.seed can ensure that the model can be reconstructed. Preferably, the user can save the returned gbm.object using save. Default is 0.5.

nTrain

An integer representing the number of cases 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.

keep.data

Logical indicating whether or not 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

Logical indicating whether or not to print out progress and performance indicators (TRUE). If this option is left unspecified for gbm.more, then it uses verbose from object. Default is FALSE.

var.names

Vector of strings of length equal to the number of columns of x containing the names of the predictor variables.

response.name

Character string label for the response variable.

group

The group to use when distribution = "pairwise".

Value

A gbm.object 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.

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. Ph.D. Dissertation. University of California at Los Angeles, Los Angeles, CA, USA. Advisor(s) Richard A. Berk. https://dl.acm.org/doi/book/10.5555/1354603.

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

Author

Greg Ridgeway gregridgeway@gmail.com

Quantile regression code developed by Brian Kriegler bk@stat.ucla.edu

t-distribution, and multinomial code developed by Harry Southworth and Daniel Edwards

Pairwise code developed by Stefan Schroedl schroedl@a9.com