mboost (version 0.4-10)

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 vector giving the degrees of freedom for the smoothing spline, either globally for all variables (when its length is one) or separately for each single covariate.

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). If dfbase = 1, a univariate linear model is used as base learner (resulting in a linear partial fit for this variable).

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")

    ### artificial example: sinus transformation
    x <- sort(runif(100)) * 10
    y <- sin(x) + rnorm(length(x), sd = 0.25)
    plot(x, y)
    ### linear model
    lines(x, fitted(lm(y ~ sin(x) - 1)), col = "red")
    ### GAM
    lines(x, fitted(gamboost(y ~ x - 1, 
                    control = boost_control(mstop = 500))), 
          col = "green")