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, ...]
mstop(x) <- value
## 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 'glmboost'
variable.names(object, which = NULL, usedonly = FALSE, ...)
## S3 method for class 'mboost'
variable.names(object, which = NULL, usedonly = FALSE, ...)
## S3 method for class 'mboost'
extract(object, what = c("design", "penalty", "lambda", "df",
"coefficients", "residuals",
"variable.names", "bnames", "offset",
"nuisance", "weights", "index", "control"),
which = NULL, ...)
## S3 method for class 'glmboost'
extract(object, what = c("design", "coefficients", "residuals",
"variable.names", "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'
risk(object, ...)
## S3 method for class 'mboost'
nuisance(object)
downstream.test(object, ...)object |
objects of class |
x |
objects of class |
model |
objects of class mboost |
newdata |
optionally, a data frame in which to look for variables with
which to predict. In case the model was fitted using the |
which |
a subset of base-learners to take into account for computing
predictions or coefficients. If |
usedonly |
logical. Indicating whether all variable names should be returned or only those selected in the boosting algorithm. |
type |
the type of prediction required. The default is on the scale
of the predictors; the alternative |
aggregate |
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
boosting iterations. |
off2int |
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). |
i |
integer. Index specifying the model to extract. If |
value |
integer. See |
return |
a logical indicating whether the changed object is returned. |
method |
a character specifying if the corrected AIC criterion or a classical (-2 logLik + k * df) should be computed. |
df |
a character specifying how degrees of freedom should be computed:
|
k |
numeric, the penalty per parameter to be used; the default
|
what |
a character specifying the quantities to |
asmatrix |
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
|
expand |
a logical indicating whether the design matrix should
be expanded (default: |
... |
additional arguments passed to callies. |
These functions can be used to extract details from fitted models.
print shows a dense representation of the model fit and
summary gives a more detailed representation.
The function 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 which argument
(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 center
= 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.
The predict function can be used to predict the status of the
response variable for new observations whereas fitted extracts
the regression fit for the observations in the learning sample. For
predict 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),
the 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
analogously to coef by setting aggregate to either
sum (default; predictions of the final iteration are given),
cumsum (predictions of all iterations are returned
simultaniously) or 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.
The [.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 i again,
these boosting steps are immediately available. Alternatively, the
same operation can be done by mstop(x) <- i.
The residuals function can be used to extract the residuals
(i.e., the negative gradient of the current iteration). resid
is is an alias for residuals.
Variable names (including those of interaction effects specified via
by in a base-learner) can be extracted using the generic
function variable.names, which has special methods for boosting
objects.
The generic 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 lambda
is set to zero. If a matrix is returned by extract one can to
set asmatrix = TRUE if the returned matrix should be coerced to
class matrix. If 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
extracted using selected(). The nuisance() method
extracts nuisance parameters from the fit that are handled internally
by the corresponding family object, see
"boost_family". The risk() function can be
used to extract the computed risk (either the "inbag" risk or
the "oobag" risk, depending on the control argument; see
boost_control).
For (generalized) linear and additive models, the AIC function
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 family
= 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 mstop).
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
via gamboost (see Hastie, 2007)). For a discussion of
the use of AIC based stopping see also Mayr, Hofner and Schmid (2012).
In addition, the general Minimum Description Length criterion
(Buehlmann and Yu, 2006) can be computed using function AIC.
Note that logLik and AIC only make sense when the
corresponding Family implements the appropriate loss
function.
downstream.test computes tests for linear models fitted via glmboost
with a likelihood based loss function and only suitable without early stopping, i.e.,
if likelihood based model converged. In order to work, the Fisher matrix must
be implemented in the Family; currently this is only the case for
family RCG.
The [.mboost function changes the original object, i.e.
gbmodel[10] changes gbmodel directly!
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.
doi: 10.1007/s00180-012-0382-5
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.
Andreas Mayr, Benjamin Hofner, and Matthias Schmid (2012). The
importance of knowing when to stop - a sequential stopping rule for
component-wise gradient boosting. Methods of Information in
Medicine, 51, 178–186.
DOI: doi: 10.3414/ME11-02-0030
gamboost, glmboost and
blackboost for model fitting.
plot.mboost for plotting methods.
cvrisk for cross-validated stopping iteration.
### 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$speed) * coef(cars.gb_centered, which="speed") # = intercept
# not asked for intercept thus not returned
coef(cars.gb_centered, which="speed")
# explicitly asked for intercept
coef(cars.gb_centered, which=c("Intercept", "speed"))
### enhance or restrict model
cars.gb <- gamboost(dist ~ speed, data = cars,
control = boost_control(mstop = 100, trace = TRUE))
cars.gb[10]
cars.gb[100, return = FALSE] # no refitting required
cars.gb[150, return = FALSE] # only iterations 101 to 150
# are newly fitted
### coefficients for optimal number of boosting iterations
coef(cars.gb[mstop(aic)])
plot(cars$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(model, what = "bnames") ## name of complete base-learner
extract(model, what = "variable.names") ## only variable names
variable.names(model) ## the same
### 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")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.