Methods for Gradient Boosting Objects
Methods for models fitted by boosting algorithms.
## S3 method for class 'glmboost': print(x, ...) ## S3 method for class 'mboost': print(x, ...)
## S3 method for class 'mboost': summary(object, ...)
## S3 method for class 'mboost': coef(object, which = NULL, aggregate = c("sum", "cumsum", "none"), ...) ## S3 method for class 'glmboost': coef(object, which = NULL, aggregate = c("sum", "cumsum", "none"), off2int = FALSE, ...)
## S3 method for class 'mboost': [(x, i, return = TRUE, ...)
## S3 method for class 'mboost': AIC(object, method = c("corrected", "classical", "gMDL"), df = c("trace", "actset"), ..., k = 2)
## S3 method for class 'mboost': mstop(object, ...) ## S3 method for class 'gbAIC': mstop(object, ...) ## S3 method for class 'cvrisk': mstop(object, ...)
## S3 method for class 'mboost': predict(object, newdata = NULL, type = c("link", "response", "class"), which = NULL, aggregate = c("sum", "cumsum", "none"), ...) ## S3 method for class 'glmboost': predict(object, newdata = NULL, type = c("link", "response", "class"), which = NULL, aggregate = c("sum", "cumsum", "none"), ...)
## S3 method for class 'mboost': fitted(object, ...)
## S3 method for class 'mboost': residuals(object, ...) ## S3 method for class 'mboost': resid(object, ...)
## S3 method for class 'mboost': extract(object, what = c("design", "penalty", "lambda", "df", "coefficients", "residuals", "bnames", "offset", "nuisance", "weights", "index", "control"), which = NULL, ...) ## S3 method for class 'glmboost': extract(object, what = c("design", "coefficients", "residuals", "bnames", "offset", "nuisance", "weights", "control"), which = NULL, asmatrix = FALSE, ...) ## S3 method for class 'blg': extract(object, what = c("design", "penalty", "index"), asmatrix = FALSE, expand = FALSE, ...)
## S3 method for class 'mboost': logLik(object, ...) ## S3 method for class 'gamboost': hatvalues(model, ...) ## S3 method for class 'glmboost': hatvalues(model, ...)
## S3 method for class 'mboost': selected(object, ...)
## S3 method for class 'mboost': nuisance(object)
- objects of class
- objects of class
- objects of class mboost
- optionally, a data frame in which to look for variables with
which to predict. In case the model was fitted using the
- a subset of base-learners to take into account for computing
predictions or coefficients. If
whichis given (as an integer vector or characters corresponding to base-learners) a list or matrix
- the type of prediction required. The default is on the scale
of the predictors; the alternative
"response"is on the scale of the response variable. Thus for a binomial model the default predictions are of log-
- a character specifying how to aggregate predictions
or coefficients of single base-learners. The default
returns the prediction or coefficient for the final number of
- logical indicating whether the offset should be added to the intercept (if there is any) or if the offset is returned as attribute of the coefficient (default).
- integer. Index specifying the model to extract. If
iis smaller than the initial
mstop, a subset is used. If
iis larger than the initial
mstop, additional boosting st
- a logical indicating whether the changed object is returned.
- a character specifying if the corrected AIC criterion or a classical (-2 logLik + k * df) should be computed.
- a character specifying how degrees of freedom should be computed:
tracedefines degrees of freedom by the trace of the boosting hat matrix and
actsetuses the number of non-zero coefficients
- numeric, the penalty per parameter to be used; the default
k = 2is the classical AIC. Only used when
method = "classical".
- a character specifying the quantities to
extract. Depending on
objectthis can be a subset of
"design"(default; design matrix),
- a logical indicating whether the the returned
matrix should be coerced to a matrix (default) or if the
returned object stays as it is (i.e., potentially a
sparse matrix). This option is only applicable if
- a logical indicating whether the design matrix should
be expanded (default:
FALSE). This is useful if ties where taken into account either manually (via argument
indexin a base-learner) or automatically
- additional arguments passed to callies.
These functions can be used to extract details from fitted models.
summary gives a more detailed representation.
coef extracts the regression coefficients of a
linear model fitted using the
glmboost function or an
additive model fitted using the
gamboost. Per default,
only coefficients of selected base-learners are returned. However, any
desired coefficient can be extracted using the
(see examples for details). Per default, the coefficient of the final
iteration is returned (
aggregate = "sum") but it is also
possible to return the coefficients from all iterations simultaniously
aggregate = "cumsum"). If
aggregate = "none" is
specified, the coefficients of the selected base-learners are
returned (see examples below).
For models fitted via
glmboost with option
= TRUE the intercept is rarely selected. However, it is implicitly
estimated through the centering of the design matrix. In this case the
intercept is always returned except
which is specified such
that the intercept is not selected. See examples below.
predict function can be used to predict the status of the
response variable for new observations whereas
the regression fit for the observations in the learning sample. For
newdata can be specified, otherwise the fitted
values are returned. If
which is specified, marginal effects of
the corresponding base-learner(s) are returned. The argument
type can be used to make predictions on the scale of the
link (i.e., the linear predictor $X\beta$),
response (i.e. $h(X\beta)$, where h is the
response function) or the
class (in case of
classification). Furthermore, the predictions can be aggregated
coef by setting
aggregate to either
sum (default; predictions of the final iteration are given),
cumsum (predictions of all iterations are returned
none (change of prediction in each
iteration). If applicable the
offset is added to the predictions.
If marginal predictions are requested the
offset is attached
to the object via
attr(..., "offset") as adding the offset to
one of the marginal predictions doesn't make much sense.
residuals function can be used to extract the residuals
(i.e., the negative gradient of the current iteration).
is is an alias for
[.mboost function can be used to enhance or restrict a given
boosting model to the specified boosting iteration
i. Note that
in both cases the original
x will be changed to reduce the
memory footprint. If the boosting model is enhanced by specifying an
index that is larger than the initial
mstop, only the missing
i - mstop steps are fitted. If the model is restricted, the
spare steps are not dropped, i.e., if we increase
these boosting steps are immediately available.
extract function can be used to extract various
characteristics of a fitted model or a base-learner. Note that the
sometimes a penalty function is returned (e.g. by
extract(bols(x), what = "penalty")) even if the estimation is
unpenalized. However, in this case the penalty paramter
is set to zero. If a matrix is returned by
extract one can to
asmatrix = TRUE if the returned matrix should be coerced to
asmatrix = FALSE one might get a sparse
matrix as implemented in package
Matrix. If one requests the
design matrix (
what = "design")
expand = TRUE expands
the resulting matrix by taking the duplicates handeled via
index into account.
The ids of base-learners selected during the fitting process can be
extracts nuisance parameters from the fit that are handled internally
by the corresponding family object, see
For (generalized) linear and additive models, the
can be used to compute both the classical AIC (only available for
familiy = Binomial() and
familiy = Poisson()) and
corrected AIC (Hurvich et al., 1998, only available when
= Gaussian() was used). Details on the used approximations for the
hat matrix can be found in Buehlmann and Hothorn (2007). The AIC is
useful for the determination of the optimal number of boosting
iterations to be applied (which can be extracted via
The degrees of freedom are either computed via the trace of the
boosting hat matrix (which is rather slow even for moderate sample
sizes) or the number of variables (non-zero coefficients) that entered
the model so far (faster but only meaningful for linear models fitted
gamboost (see Hastie, 2007)).
In addition, the general Minimum Description Length criterion
(Buehlmann and Yu, 2006) can be computed using function
AIC only make sense when the
Family implements the appropriate loss
[.mboost function changes the original object, i.e.
The coefficients resulting from boosting with family
Binomial are $1/2$ of the coefficients of a logit
model obtained via
glm. This is due to the internal
recoding of the response to $-1$ and $+1$ (see
Clifford M. Hurvich, Jeffrey S. Simonoff and Chih-Ling Tsai (1998), Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society, Series B, 20(2), 271--293.
Peter Buehlmann and Torsten Hothorn (2007), Boosting algorithms: regularization, prediction and model fitting. Statistical Science, 22(4), 477--505.
Trevor Hastie (2007), Discussion of ``Boosting algorithms: Regularization, prediction and model fitting'' by Peter Buehlmann and Torsten Hothorn. Statistical Science, 22(4), 505.
Peter Buehlmann and Bin Yu (2006), Sparse boosting. Journal of Machine Learning Research, 7, 1001--1024.
### a simple two-dimensional example: cars data cars.gb <- glmboost(dist ~ speed, data = cars, control = boost_control(mstop = 2000), center = FALSE) cars.gb ### initial number of boosting iterations mstop(cars.gb) ### AIC criterion aic <- AIC(cars.gb, method = "corrected") aic ### extract coefficients for glmboost coef(cars.gb) coef(cars.gb, off2int = TRUE) # offset added to intercept coef(lm(dist ~ speed, data = cars)) # directly comparable cars.gb_centered <- glmboost(dist ~ speed, data = cars, center = TRUE) selected(cars.gb_centered) # intercept never selected coef(cars.gb_centered) # intercept implicitly estimated # and thus returned ## intercept is internally corrected for mean-centering - mean(cars$speed) * coef(cars.gb_centered, which="speed") # = intercept # not asked for intercept thus not returned coef(cars.gb_centered, which="speed") # explicitly asked for intercept coef(cars.gb_centered, which=c("Intercept", "speed")) ### enhance or restrict model cars.gb <- gamboost(dist ~ speed, data = cars, control = boost_control(mstop = 100, trace = TRUE)) cars.gb cars.gb[100, return = FALSE] # no refitting required cars.gb[150, return = FALSE] # only iterations 101 to 150 # are newly fitted ### coefficients for optimal number of boosting iterations coef(cars.gb[mstop(aic)]) plot(cars$dist, predict(cars.gb[mstop(aic)]), ylim = range(cars$dist)) abline(a = 0, b = 1) ### example for extraction of coefficients set.seed(1907) n <- 100 x1 <- rnorm(n) x2 <- rnorm(n) x3 <- rnorm(n) x4 <- rnorm(n) int <- rep(1, n) y <- 3 * x1^2 - 0.5 * x2 + rnorm(n, sd = 0.1) data <- data.frame(y = y, int = int, x1 = x1, x2 = x2, x3 = x3, x4 = x4) model <- gamboost(y ~ bols(int, intercept = FALSE) + bbs(x1, center = TRUE, df = 1) + bols(x1, intercept = FALSE) + bols(x2, intercept = FALSE) + bols(x3, intercept = FALSE) + bols(x4, intercept = FALSE), data = data, control = boost_control(mstop = 500)) coef(model) # standard output (only selected base-learners) coef(model, which = 1:length(variable.names(model))) # all base-learners coef(model, which = "x1") # shows all base-learners for x1 cf1 <- coef(model, which = c(1,3,4), aggregate = "cumsum") tmp <- sapply(cf1, function(x) x) matplot(tmp, type = "l", main = "Coefficient Paths") cf1_all <- coef(model, aggregate = "cumsum") cf1_all <- lapply(cf1_all, function(x) x[, ncol(x)]) # last element ## same as coef(model) cf2 <- coef(model, aggregate = "none") cf2 <- lapply(cf2, rowSums) # same as coef(model) ### example continued for extraction of predictions yhat <- predict(model) # standard prediction; here same as fitted(model) p1 <- predict(model, which = "x1") # marginal effects of x1 orderX <- order(data$x1) ## rowSums needed as p1 is a matrix plot(data$x1[orderX], rowSums(p1)[orderX], type = "b") ## better: predictions on a equidistant grid new_data <- data.frame(x1 = seq(min(data$x1), max(data$x1), length = 100)) p2 <- predict(model, newdata = new_data, which = "x1") lines(new_data$x1, rowSums(p2), col = "red") ### extraction of model characteristics extract(model, which = "x1") # design matrices for x1 extract(model, what = "penalty", which = "x1") # penalty matrices for x1 extract(model, what = "lambda", which = "x1") # df and corresponding lambda for x1 ## note that bols(x1, intercept = FALSE) is unpenalized ### extract from base-learners extract(bbs(x1), what = "design") extract(bbs(x1), what = "penalty") ## weights and lambda can only be extracted after using dpp weights <- rep(1, length(x1)) extract(bbs(x1)$dpp(weights), what = "lambda")