mboost (version 2.1-0)

glmboost: Gradient Boosting with Component-wise Linear Models

Description

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

Usage

## S3 method for class 'formula':
glmboost(formula, data = list(), weights = NULL,
          na.action = na.pass, contrasts.arg = NULL,
          center = TRUE, control = boost_control(), ...)
## S3 method for class 'matrix':
glmboost(x, y, center = TRUE, control = boost_control(), ...)
## S3 method for class 'default':
glmboost(x,  ...)
## S3 method for class 'glmboost':
plot(x, main = deparse(x$call), col = NULL,
                        off2int = FALSE, ...)

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.

contrasts.arg

a list, whose entries are contrasts suitable for input to the contrasts replacement function and whose names are the names of columns of data containing factors. See

na.action

a function which indicates what should happen when the data contain NAs.

center

logical indicating of the predictor variables are centered before fitting.

control

a list of parameters controlling the algorithm.

x

design matrix or an object of class glmboost for plotting. Sparse matrices of class Matrix can be used as well.

y

vector of responses.

main

a title for the plot.

col

(a vector of) colors for plotting the lines representing the coefficient paths.

off2int

logical indicating whether the offset should be added to the intercept (if there is any) or if the offset is neglected for plotting (default).

...

additional arguments passed to mboost_fit, including weights, offset, family and control. For default values see

Value

• An object of class glmboost with print, coef, AIC and predict methods being available. For inputs with longer variable names, you might want to change par("mai") before calling the plot method of glmboost objects visualizing the coefficients path.

Details

A (generalized) linear model is fitted using a boosting algorithm based on component-wise univariate linear models. The fit, i.e., the regression coefficients, can be interpreted in the usual way. The methodology is described in Buehlmann and Yu (2003), Buehlmann (2006), and Buehlmann and Hothorn (2007).

References

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

Peter Buehlmann (2006), Boosting for high-dimensional linear models. The Annals of Statistics, 34(2), 559--583.

Peter Buehlmann and Torsten Hothorn (2007), Boosting algorithms: regularization, prediction and model fitting. Statistical Science, 22(4), 477--505.

Torsten Hothorn, Peter Buehlmann, Thomas Kneib, Mattthias Schmid and Benjamin Hofner (2010), Model-based Boosting 2.0. Journal of Machine Learning Research, 11, 2109 -- 2113.

See Also

mboost for the generic boosting function and gamboost for boosted additive models and blackboost for boosted trees. See cvrisk for cross-validated stopping iteration. Furthermore see boost_control, Family and methods

Examples

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

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

    ### plot fit
    layout(matrix(1:2, ncol = 2))
    plot(dist ~ speed, data = cars)
    lines(cars$speed, predict(cars.gb), col = "red")

    ### now we center the design matrix for
    ### much quicker "convergence"
    cars.gb_centered <- glmboost(dist ~ speed, data = cars,
                                 control = boost_control(mstop = 2000),
                                 center = TRUE)
    par(mfrow=c(1,2))
    plot(cars.gb, main="without centering")
    plot(cars.gb_centered, main="with centering")

    ### 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")

    ### plot coefficient path of glmboost
    par(mai = par("mai") * c(1, 1, 1, 2.5))
    plot(cars.gb)

    ### sparse high-dimensional example
    library("Matrix")
    n <- 100
    p <- 10000
    ptrue <- 10
    X <- Matrix(0, nrow = n, ncol = p)
    X[sample(1:(n * p), floor(n * p / 20))] <- runif(floor(n * p / 20))
    beta <- numeric(p)
    beta[sample(1:p, ptrue)] <- 10
    y <- drop(X %*% beta + rnorm(n, sd = 0.1))
    mod <- glmboost(y = y, x = X, center = TRUE) ### mstop needs tuning
    coef(mod, which = which(beta > 0))