mboost: Model-Based Boosting

Description

Functional gradient descent algorithm (boosting) for optimizing general risk functions utilizing component-wise (penalised) least squares estimates or regression trees as base-learners for fitting generalized linear, additive and interaction models to potentially high-dimensional data.

Details

This package is intended for modern regression modelling and stands in-between classical generalized linear and additive models, as for example implemented by lm, glm, or gam, and machine-learning approaches for complex interactions models, most prominently represented by gbm and randomForest.

All functionality in this package is based on the generic implementation of the optimization algorithm (function mboost_fit) that allows for fitting linear, additive, and interaction models (and mixtures of those) in low and high dimensions. The response may be numeric, binary, ordered, censored or count data.

Both theory and applications are discussed by Buehlmann and Hothorn (2007). UseRs without a basic knowledge of boosting methods are asked to read this introduction before analyzing data using this package. The examples presented in this paper are available as package vignette mboost_illustrations.

Note that the model fitting procedures in this package DO NOT automatically determine an appropriate model complexity. This task is the responsibility of the data analyst.

NEWS in 2.2-series

Starting from version 2.2, the default for the degrees of freedom has changed. Now the degrees of freedom are (per default) defined as

df(λ) = trace(2S - S'S),

with smoother matrix S = X(X'X + λ K)^(-1) X (see Hofner et al., 2011). Earlier versions used the trace of the smoother matrix \mathrm{df}(λ) = \mathrm{trace}(S) as degrees of freedom. One can change the deployed definition using options(mboost_dftraceS = TRUE) (see also B. Hofner et al., 2011 and bols).

Other important changes inlclude:

• We switched from packages multicore and snow to parallel

• We changed the behavior of bols(x, intercept = FALSE) when x is a factor: now the intercept is simply dropped from the design matrix and the coding can be specified as usually for factors. Addtionally, a new contrast is introduced: "contr.dummy" (see bols for details).

• We changed the computation of B-spline basis at the boundaries; B-splines now also use equidistant knots in the boundaries (per default).

For more changes see NEWS file.

NEWS in 2.1-series

In the 2.1 series, we added multiple new base-learners including bmono (monotonic effects), brad (radial basis functions) and bmrf (Markov random fields), and extended bbs to incorporate cyclic splines (via argument cyclic = TRUE). We also changed the default df for bspatial to 6.

Starting from this version, we now also automatically center the variables in glmboost (argument center = TRUE).

A complete list of changes can be found in the NEWS file.

NEWS in 2.0-series

Version 2.0 comes with new features, is faster and more accurate in some aspects. In addition, some changes to the user interface were necessary: Subsetting mboost objects changes the object. At each time, a model is associated with a number of boosting iterations which can be changed (increased or decreased) using the subset operator.

The center argument in bols was renamed to intercept. Argument z renamed to by.

The base-learners bns and bss are deprecated and replaced by bbs (which results in qualitatively the same models but is computationally much more attractive).

New features include new families (for example for ordinal regression) and the which argument to the coef and predict methods for selecting interesting base-learners. Predict methods are much faster now.

The memory consumption could be reduced considerably, thanks to sparse matrix technology in package Matrix. Resampling procedures run automatically in parallel on OSes where parallelization via package parallel is available.

The most important advancement is a generic implementation of the optimizer in function mboost_fit.

Author(s)

Torsten Hothorn Torsten.Hothorn@R-project.org,
Peter Buehlmann, Thomas Kneib, Matthias Schmid and Benjamin Hofner

References

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.

Benjamin Hofner, Torsten Hothorn, Thomas Kneib, and Matthias Schmid (2011), A framework for unbiased model selection based on boosting. Journal of Computational and Graphical Statistics, 20, 956–971.

Benjamin Hofner, Andreas Mayr, Nikolay Robinzonov and Matthias Schmid (2012). Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost. Department of Statistics, Technical Report No. 120.
http://epub.ub.uni-muenchen.de/12754/

Available as vignette via: vignette(package = "mboost", "mboost_tutorial")

See Also

The main fitting functions include:
gamboost for boosted (generalized) additive models, glmboost for boosted linear models and blackboost for boosted trees.
See there for more details and further links.

Examples

  data("bodyfat")
  set.seed(290875)

  ### model conditional expectation of DEXfat given
  model <- mboost(DEXfat ~
      bols(age) +                 ### a linear function of age
      btree(hipcirc, waistcirc) + ### a non-linear interaction of
                                  ### hip and waist circumference
      bbs(kneebreadth),           ### a smooth function of kneebreadth
      data = bodyfat, control = boost_control(mstop = 100))

  ### bootstrap for assessing `optimal' number of boosting iterations
  cvm <- cvrisk(model, papply = lapply)

  ### restrict model to mstop(cvm)
  model[mstop(cvm), return = FALSE]
  mstop(model)

  ### plot age and kneebreadth
  layout(matrix(1:2, nc = 2))
  plot(model, which = c("age", "kneebreadth"))

  ### plot interaction of hip and waist circumference
  attach(bodyfat)
  nd <- expand.grid(hipcirc = h <- seq(from = min(hipcirc),
                                  to = max(hipcirc),
                                  length = 100),
                    waistcirc = w <- seq(from = min(waistcirc),
                                  to = max(waistcirc),
                                  length = 100))
  plot(model, which = 2, newdata = nd)
  detach(bodyfat)

  ### customized plot
  layout(1)
  pr <- predict(model, which = "hip", newdata = nd)
  persp(x = h, y = w, z = matrix(pr, nrow = 100, ncol = 100))