mboost (version 2.9-9)

mboost-package: mboost: Model-Based Boosting


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


NEWS in 2.9-series

Series 2.9 provides a new family (RCG), uses partykit::ctree instead of party::ctree to be more flexible, allows for multivariate negative gradients, and leave-one-out crossvalidation. Further minor changes were introduces and quite some bugs were fixed.

For more details and other changes see
news(Version >= "2.9-0", package = "mboost")

NEWS in 2.8-series

Series 2.8 allows to fit models with zero boosting steps (i.e., models containing only the offset). Furthermore, cross-validation can now also select a model without base-learners. In a Binomial family one can now specifiy links via make.link. With Binomial(type = "glm") an alternative implementation of Binomial models is now existing and defines the model along the lines of the glm implementation. Additionally, it works not only with a two-level factor but also with a two-column matrix containing the number of successes and number of failures. Finally, a new base-learner bkernel for kernel boosting was added. The references were updated and a lot of bugs fixed.

For more details and other changes see
news(Version >= "2.8-0", package = "mboost")

NEWS in 2.7-series

Series 2.7 provides a new family (Cindex), variable importance measures (varimp) and improved plotting facilities. The manual was updated in various places, vignettes were improved and a lot of bugs were fixed.

For more details and other changes see
news(Version >= "2.7-0", package = "mboost")

NEWS in 2.6-series

Series 2.6 includes a lot of bug fixes and improvements. Most notably, the development of the package is now hosted entirely on github in the project boost-R/mboost. Furthermore, the package is now maintained by Benjamin Hofner.

For more details and other changes see
news(Version >= "2.6-0", package = "mboost")

NEWS in 2.5-series

Crossvaliation does not stop on errors in single folds anymore an was sped up by setting mc.preschedule = FALSE if parallel computations via mclapply are used. The plot.mboost function is now documented. Values outside the boundary knots are now better handeled (forbidden during fitting, while linear extrapolation is used for prediction). Further perfomance improvements and a lot of bug fixes have been added.

For more details and other changes see
news(Version >= "2.5-0", package = "mboost")

NEWS in 2.4-series

Bootstrap confidence intervals have been implemented in the novel confint function. The stability selection procedure has now been moved to a stand-alone package called stabs, which now also implements an iterface to use stability selection with other fitting functions. A generic function for "mboost" models is implemented in mboost.

For more details and other changes see
news(Version >= "2.4-0", package = "mboost")

NEWS in 2.3-series

The stability selection procedure has been completely rewritten and improved. The code base is now extensively tested. New options allow for a less conservative error control.

Constrained effects can now be fitted using quadratic programming methods using the option type = "quad.prog" (default) for highly improved speed. Additionally, new constraints have been added.

Other important changes include:

  • A new replacement function mstop(mod) <- i as an alternative to mod[i] was added (as suggested by Achim Zeileis).

  • We added new families Hurdle and Multinomial.

  • We added a new argument stopintern for internal stopping (based on out-of-bag data) during fitting to boost_control.

For more details and other changes see
news(Version >= "2.3-0", package = "mboost")

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 $$\mathrm{df}(\lambda) = \mathrm{trace}(2S - S^{\top}S),$$ with smoother matrix \(S = X(X^{\top}X + \lambda K)^{-1} X\) (see Hofner et al., 2011). Earlier versions used the trace of the smoother matrix \(\mathrm{df}(\lambda) = \mathrm{trace}(S)\) as degrees of freedom. One can change the old definition using options(mboost_dftraceS = TRUE) (see also B. Hofner et al., 2011 and bols).

Other important changes include:

  • 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. Additionally, 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 details and other changes see
news(Version >= "2.2-0" & Version < "2.3-0", package = "mboost")

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).

For more details and other changes see
news(Version >= "2.1-0" & Version < "2.2-0", package = "mboost")

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.

For more details and other changes see
news(Version >= "2.0-0" & Version < "2.1-0", package = "mboost")


Torsten Hothorn,Peter Buehlmann, Thomas Kneib, Matthias Schmid and Benjamin Hofner <Benjamin.Hofner@pei.de>


This package is intended for modern regression modeling 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.

A description of novel features that were introduced in version 2.0 is given in Hothorn et. al (2010).

Hofner et al. (2014) present a comprehensive hands-on tutorial for using the package mboost, which is also available as vignette(package = "mboost", "mboost_tutorial").

Ben Taieba and Hyndman (2013) used this package for fitting their model in the Kaggle Global Energy Forecasting Competition 2012. The corresponding research paper is a good starting point when you plan to analyze your data using mboost.


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, Matthias 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 (2014). Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost. Computational Statistics, 29, 3--35.

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

Souhaib Ben Taieba and Rob J. Hyndman (2014), A gradient boosting approach to the Kaggle load forecasting competition. International Journal of Forecasting, 30, 382--394.

See Also

The main fitting functions include:

  • gamboost for boosted (generalized) additive models,

  • glmboost for boosted linear models and

  • blackboost for boosted trees.

Model tuning is done via cross-validation as implemented in cvrisk.
See there for more details and further links.


Run this code

  data("bodyfat", package = "TH.data")

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

  ### 10-fold cv for assessing `optimal' number of boosting iterations
  cvm <- cvrisk(model, papply = lapply, 
                folds = cv(model.weights(model), type = "kfold"))
  ### probably needs larger initial mstop but the
  ### CRAN team is picky about running times for examples

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

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

  ### plot interaction of hip and waist circumference
  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)

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

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