TDboost {TDboost}

TDboost Tweedie Regression Modeling

Description

Fits TDboost Tweedie Regression models.

Usage

TDboost(formula = formula(data),
    distribution = list(name="EDM",alpha=1.5),
    data = list(),
    weights,
    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)

TDboost.fit(x,y,
        offset = NULL,
        misc = NULL,
        distribution = list(name="EDM",alpha=1.5),
        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)

TDboost.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. The formula may include an offset term (e.g. y~offset(n)+x). If keep.data=FALSE in the initial call to TDboost then it is the user's responsibility to resupply the offset to TDboost.more.

distribution

a list with a component name specifying the distribution and any additional parameters needed. Tweedie regression is available and distribution must a list of the form list(name="EDM",alpha=1.5) where alpha is the index parameter that must be in (1,2]. When alpha=2, the distribution reduces to gamma. The current version's Tweedie regression methods do not handle non-constant weights and will stop.

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 TDboost is called. If keep.data=TRUE in the initial call to TDboost then TDboost stores a copy with the object. If keep.data=FALSE then subsequent calls to TDboost.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. Must be positive but do not need to be normalized. If keep.data=FALSE in the initial call to TDboost then it is the user's responsibility to resupply the weights to TDboost.more.

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

train.fraction

The first train.fraction * nrows(data) observations are used to fit the TDboost 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 TDboost.more faster at the cost of storing an extra copy of the dataset.

object

a TDboost object created from an initial call to TDboost.

n.new.trees

the number of additional trees to add to object.

verbose

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

x, y

For TDboost.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.

offset

a vector of values for the offset

misc

For TDboost.fit: misc is an R object that is simply passed on to the TDboost engine.

w

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

var.names

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

Details

This package implements a regression tree based gradient boosting estimator for nonparametric multiple Tweedie regression. The code is a modified version of gbm library originally written by Greg Ridgeway.

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, TDboost offers additional features including the out-of-bag estimator for the optimal number of iterations, the ability to store and manipulate the resulting TDboost object.

TDboost.fit provides the link between R and the C++ TDboost engine. TDboost is a front-end to TDboost.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 TDboost.fit. For general practice TDboost is preferable.

Value

TDboost, TDboost.fit, and TDboost.more return a TDboost.object.

Author(s)

Yi Yang [e-mail], Wei Qian [e-mail] and Hui Zou [e-mail]

References

Yang, Y., Qian, W. and Zou, H. (2013), “A Boosted Tweedie Compound Poisson Model for Insurance Premium” Preprint.

G. Ridgeway (1999). “The state of boosting,” Computing Science and Statistics 31:172-181.

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.

See Also

TDboost.object, TDboost.perf, plot.TDboost, predict.TDboost, summary.TDboost,

Examples

data(FHT)
# training on data1
TDboost1 <- TDboost(Y~X1+X2+X3+X4+X5+X6,         # formula
    data=data1,                   # dataset
    var.monotone=c(0,0,0,0,0,0), # -1: monotone decrease,
                                 # +1: monotone increase,
                                 #  0: no monotone restrictions
    distribution=list(name="EDM",alpha=1.5),
                                 # specify Tweedie index parameter
    n.trees=3000,                # number of trees
    shrinkage=0.005,             # 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
    cv.folds = 5,                # do 5-fold cross-validation
    keep.data=TRUE,              # keep a copy of the dataset with the object
    verbose=TRUE)                # print out progress

# print out the optimal iteration number M
best.iter <- TDboost.perf(TDboost1,method="test")
print(best.iter)

# check performance using 5-fold cross-validation
best.iter <- TDboost.perf(TDboost1,method="cv")
print(best.iter)

# plot the performance
# plot variable influence
summary(TDboost1,n.trees=1)         # based on the first tree
summary(TDboost1,n.trees=best.iter) # based on the estimated best number of trees

# making prediction on data2
f.predict <- predict.TDboost(TDboost1,data2,best.iter)

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

# create marginal plots
# plot variable X1 after "best" iterations
plot.TDboost(TDboost1,1,best.iter)
# contour plot of variables 1 and 3 after "best" iterations
plot.TDboost(TDboost1,c(1,3),best.iter)

# do another 20 iterations
TDboost2 <- TDboost.more(TDboost1,20,
                 verbose=FALSE) # stop printing detailed progress

# fit a gamma model (when alpha = 2.0)
data2 <- data1[data1$Y!=0,]
TDboost3 <- TDboost(Y~X1+X2+X3+X4+X5+X6,         # formula
    data=data2,                   # dataset
    distribution=list(name="EDM",alpha=2.0),
    n.trees=3000, 				 # number of trees
    train.fraction = 0.5,        # fraction of data for training,
    verbose=TRUE)                # print out progress
best.iter2 <- TDboost.perf(TDboost3,method="test")