mboost (version 0.4-6)

glmboost: Gradient Boosting with Componentwise Linear Models

Description

Gradient boosting for optimizing arbitrary loss functions where componentwise linear models are utilized as base learners.

Usage

## S3 method for class 'formula':
glmboost(formula, data = list(), weights = NULL, ...)
## S3 method for class 'matrix':
glmboost(x, y, weights = NULL, ...)
glmboost_fit(object, 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.

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 glmboost with print, coef, AIC and predict methods being available.

Details

A (generalized) linear model is fitted using a boosting algorithm based on componentwise univariate linear models. The fit, i.e., the regression coefficients, can be interpreted in the usual way. The methodology is described in Buhlmann and Yu (2003) and Buhlmann (2006).

The function glmboost_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 (2006), Boosting for high-dimensional linear models. The Annals of Statistics, 34.

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

Examples

### a simple two-dimensional example: cars data
    cars.gb <- glmboost(dist ~ speed, data = cars, 
                        control = boost_control(mstop = 5000))
    cars.gb

    ### coefficients should coincide
    coef(cars.gb) + c(cars.gb$offset, 0)
    coef(lm(dist ~ speed, data = cars))

    ### plot fit
    plot(dist ~ speed, data = cars)
    lines(cars$speed, predict(cars.gb), col = "red")

    ### alternative loss function: absolute loss
    cars.gbl <- glmboost(dist ~ speed, data = cars, 
                         control = boost_control(mstop = 5000), 
                         family = Laplace())
    cars.gbl

    coef(cars.gbl) + c(cars.gbl$offset, 0)
    lines(cars$speed, predict(cars.gbl), col = "green")

    ### Huber loss with adaptive choice of delta
    cars.gbh <- glmboost(dist ~ speed, data = cars, 
                         control = boost_control(mstop = 5000), 
                         family = Huber())

    lines(cars$speed, predict(cars.gbh), col = "blue")
    legend("topleft", col = c("red", "green", "blue"), lty = 1,
           legend = c("Gaussian", "Laplace", "Huber"), bty = "n")