methods {mboost} | R Documentation |
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)
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 |
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 |
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 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
.
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.
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"
.
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)).
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.
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
Binomial
).
The [.mboost
function changes the original object, i.e.
gbmodel[10]
changes gbmodel
directly!
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.
gamboost
, glmboost
and
blackboost
for model fitting. See 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 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")