mboost (version 0.4-6)

gamboost: Gradient Boosting with Componentwise Smoothing Splines

Description

Gradient boosting for optimizing arbitrary loss functions where componentwise smoothing splines are utilized as base learners.

Usage

## S3 method for class 'formula':
gamboost(formula, data = list(), weights = NULL, ...)
## S3 method for class 'matrix':
gamboost(x, y, weights = NULL, ...)
gamboost_fit(object, dfbase = 4, family = GaussReg(), 
             control = boost_control(), weights = NULL)

Arguments

formula

a symbolic description of the model to be fit.

data

a data frame containing the variables in the model.

weights

an optional vector of weights to be used in the fitting process.

x

design matrix.

y

vector of responses.

object

an object of class boost_data, see boost_dpp.

dfbase

an integer giving the degrees of freedom for the smoothing spline.

family

an object of class boost_family-class, implementing the negative gradient corresponding to the loss function to be optimized, by default, squared error loss

control

an object of class boost_control.

...

additional arguments passed to callies.

Value

• An object of class gamboost with print, AIC and predict methods being available.

Details

A (generalized) additive model is fitted using a boosting algorithm based on componentwise univariate smoothing splines. The methodology is described in Buhlmann and Yu (2003).

The function gamboost_fit provides access to the fitting procedure without data pre-processing, e.g. for cross-validation.

References

Peter Buhlmann and Bin Yu (2003), Boosting with the L2 loss: regression and classification. Journal of the American Statistical Association, 98, 324--339.

Peter Buhlmann and Torsten Hothorn (2006), Boosting: A statistical perspective. Submitted manuscript.

Examples

### a simple two-dimensional example: cars data
    cars.gb <- gamboost(dist ~ speed, data = cars, dfbase = 4, 
                        control = boost_control(mstop = 50))
    cars.gb
    AIC(cars.gb, method = "corrected")

    ### plot fit for mstop = 1, ..., 50
    plot(dist ~ speed, data = cars)    
    tmp <- sapply(1:mstop(AIC(cars.gb)), function(i)
        lines(cars$speed, predict(cars.gb[i]), col = "red"))          
    lines(cars$speed, predict(smooth.spline(cars$speed, cars$dist),
                              cars$speed)$y, col = "green")