mfboost: Model-based Boosting for Manifold Valued Object Data
In Almond-S/manifoldboost: Boosting Regression Models for Manifold Valued Data
mfboost R Documentation
Model-based Boosting for Manifold Valued Object Data
Description
An interface for model-based gradient boosting when response observations
are naturally represented as vectors, matrices,
or smooth potentially multidimensional functions.
The function is a wrapper for the function mboost
in the model-based boosting package mboost via its functional pendant
FDboost from the FDboost package.
For manifold valued responses, like shapes, appropriate loss functions
can be fitted using an mfFamily.
Usage
mfboost(formula, obj.formula = NULL, data = NULL, family = Gaussian(), ...)
Arguments
formula
a symbolic description of the model formula y ~ ...
on covariate level, i.e. specified as if the response was scalar,
where y refers to an object (in data) containing all response data.
obj.formula
intrinsic model formula for the internal representation
of the response. E.g., for a functional response y_i(t) typically use
value ~ bbs(t) to obtain smooth effects over t, where value
refers to the response evaluations (in y). See details for further
information.
data
a list containing the variables in the model.
The response should be either provided as tbl_cube (regular case) or
as list of tbl_cubes or data.frames (irregular case). See details.
family
an mfFamily object.
...
additional arguments passed to FDboost/mboost.
Details
While the response observations y_i and the corresponding predictions
μ_i might live on a non-linear manifold M, they are modeled with
an additive predictor η_i living in a linear space by
μ_i = g_p(η_i) = g_p(∑_j h_j(x_i))
where g_p is a response function, which might depend on a pole p \in M
and is typically chosen as g_p = Exp_p, the manifold exponential function
at p. The additive predictor η_i is composed of partial effects
h_j(x_i) as provided by the R packages mboost and FDboost,
but potentially constraining them to a respective linear subspace, e.g.
corresponding to the tangent space at p.
For further details on available covariate effects see
FDboost and the baselearners
help of mboost.
Computationally, it might make a huge difference whether response observations
are measured on a common regular grid or on irregular individual grids. In the
regular case, the linear array model can be utilized
(Brockhaus et al. 2015, Currie et al. 2006) for the design
matrix and the regular structure might also be used to speed up pole and
gradient computation.
This distinction is reflected - and controlled by - the data format and
in particular the format the response is provided in. For a data set with
N observations, data should be
provided as list containing scalar covariate vectors (of length N).
The response should be contained as follows:
in the regular case, the response should be
a tbl_cube with response
values as measures and remaining variables contained in
obj.formula as dimensions, listed according to the covariates.
in the irregular case, the response should be a data.frame
(or list) with the response variables appearing in the obj.formula.
for backward compatibility, data can also be in the format of
FDboost, i.e., data is again a list
and the response is provided in separate list elements:
in the regular case, the response measurements are provided as matrix
with N rows corresponding to the observations and the columns
containing all measurements in long format and the dim and obj.formula
variables as vectors along the columns of the matrix.
in the irregular case, the columns of the last irregular option above
are just separately added to the list.
Value
An object of class mfboost inheriting from FDboost and
mboost.
Brockhaus, S., Scheipl, F., Hothorn, T. and Greven, S. (2015):
The functional linear array model. Statistical Modelling, 15(3), 279-300.
Currie, I.D., Durban, M. and Eilers P.H.C. (2006):
Generalized linear array models with applications to multidimensional smoothing.
Journal of the Royal Statistical Society, Series B-Statistical Methodology, 68(2), 259-280.
See Also
mfFamily,
factorize, data example cells
Examples
# modeling the FORM/SIZE-AND-SHAPE of IRREGULAR curves -------------------
# load irregular cell data
data("cells", package = "manifoldboost")
# subsample (one for each covariate combination)
cellsub <- as.data.frame(cells[-which(names(cells)=="response")])
cellsub$myd <- factor(with(cellsub,
paste0("a=", a, " r=", r, " b=", b, " m=", m)))
subids <- match(unique(cellsub$myd), cellsub$myd)
cellsub <- as.list(cellsub[subids, ])
cellsub$response <- cells$response[as.numeric(cells$response$id) %in% subids, ]
# fit model
cell_model <- mfboost(
formula = response ~ bbsc(a, df = 3, knots = 5) +
bbsc(r, df = 3, knots = 5) +
bbsc(b, df = 3, knots = 5) +
bbsc(m, df = 3, knots = 5),
obj.formula = value^dim ~
bbs(arg, df = 1, differences = 0, knots = 5,
boundary.knots = c(0,1), cyclic = TRUE) | id,
data = cellsub,
family = PlanarSizeShapeL2(
weight_fun = trapez_weights,
arg_range = c(0,1)),
control = boost_control(mstop = 300)
)
# # cross-validation
# set.seed(9382)
# cell_cv <- cvrisk(cell_model,
# folds = cvLong(
# id = cell_model$id,
# weights = cell_model$`(weights)`,
# type = "kfold"),
# grid = 0:mstop(cell_model))
# cell_model[mstop(cell_cv)]
# plot first four predictions
par(mfrow = c(2,2), mar = rep(2, 4) )
plot(cell_model, ids = 1:4, t = "l",
main = cellsub$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("intercept", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# compare with data
plot(cell_model, ids = 1:4, t = "l", y0_ = cell_model$family@mf$y_[1:4],
main = cellsub$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("observation", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# predict dense cells on grids
cellgrid <- cellsub
cellgrid$response <- with(cellgrid$response, expand.grid(
id = unique(id),
arg = seq(0,1, len = 100),
dim = unique(dim),
value = NA))
cellgrid$response$value <- predict(cell_model,
newdata = cellgrid, type = "response")
# factorize effects
cell_fac <- factorize(cell_model)
vimp <- varimp(cell_fac$cov)
plot(vimp, auto.key = FALSE)
# plot two most important effect directions
this <- cell_fac$cov$which(head(names(vimp)[order(vimp, decreasing = TRUE)], 2))
par(mfcol = c(2,2))
plot(cell_fac$resp, which = this, y0_par = list(type="l"))
plot(cell_fac$cov, which = this)
# modeling the SHAPE of REGULAR curves -------------------
# load regular cell data
data("cellr", package = "manifoldboost")
# subsample (one for each covariate combination)
cellsub <- as.data.frame(cellr[-which(names(cellr)=="response")])
cellsub$myd <- factor(with(cellsub,
paste0("a=", a, " r=", r, " b=", b, " m=", m)))
subids <- match(unique(cellsub$myd), cellsub$myd)
cellsub <- as.list(cellsub[subids, ])
cellsub$response <- cellr$response
cellsub$response$dims$id <- ordered(cellsub$response$dims$id[subids],
levels = unique(cellsub$response$dims$id[subids]))
cellsub$response$mets$value <- cellsub$response$mets$value[,,subids]
class(cellsub$response) <- "tbl_cube"
# fit SHAPE model
cell_model <- mfboost(
formula = response ~ bbsc(a, df = 3, knots = 5) +
bbsc(r, df = 3, knots = 5) +
bbsc(b, df = 3, knots = 5) +
bbsc(m, df = 3, knots = 5),
obj.formula = value^dim ~
bbs(arg, df = 1, differences = 0, knots = 5,
boundary.knots = c(0,70), cyclic = TRUE) | id,
data = cellsub,
family = PlanarShapeL2(),
control = boost_control(mstop = 100)
)
# # cross-validation
# set.seed(8768)
# cell_cv <- cvrisk(cell_model,
# folds = cvMa(ydim = cell_model$ydim,
# type = "kfold"),
# grid = 0:mstop(cell_model))
# cell_model[mstop(cell_cv)]
# plot first four predictions
par(mfrow = c(2,2), mar = rep(2, 4) )
plot(cell_model, ids = 1:4, t = "l",
main = cells$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("intercept", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# compare with data
plot(cell_model, ids = 1:4, t = "l", y0_ = cell_model$family@mf$y_[1:4],
main = cellsub$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("observation", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# predict dense cells on grids
cellgrid <- cellsub
cellgrid$response <- cubelyr::tbl_cube(
dimensions = list(
id = cellsub$response$dims$id,
arg = seq(0,70, len = 100),
dim = unique(cellsub$response$dims$dim)
),
measures = list(
value = array(NA, dim = c(29, 100, 2))))
cellgrid$response$mets$value <- array(predict(cell_model,
newdata = cellgrid, type = "response"),
dim = c(29,100,2))
for(i in 1:4)
plot(cellgrid$response$mets$value[i,,], t = "l")
# factorize effects
cell_fac <- factorize(cell_model)
vimp <- varimp(cell_fac$cov)
plot(vimp, auto.key = FALSE)
# plot two most important effect directions
this <- cell_fac$cov$which(head(names(vimp)[order(vimp, decreasing = TRUE)], 2))
par(mfcol = c(2,2))
plot(cell_fac$resp, which = this, y0_par = list(type="l"))
plot(cell_fac$cov, which = this)
Almond-S/manifoldboost documentation built on June 23, 2022, 11:06 a.m.
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| mfboost | R Documentation |
Model-based Boosting for Manifold Valued Object Data
Description
An interface for model-based gradient boosting when response observations
are naturally represented as vectors, matrices,
or smooth potentially multidimensional functions.
The function is a wrapper for the function mboost
in the model-based boosting package mboost via its functional pendant
FDboost from the FDboost package.
For manifold valued responses, like shapes, appropriate loss functions
can be fitted using an mfFamily.
Usage
mfboost(formula, obj.formula = NULL, data = NULL, family = Gaussian(), ...)
Arguments
formula |
a symbolic description of the model formula |
obj.formula |
intrinsic model formula for the internal representation
of the response. E.g., for a functional response y_i(t) typically use
|
data |
a list containing the variables in the model.
The response should be either provided as |
family |
an |
... |
additional arguments passed to |
Details
While the response observations y_i and the corresponding predictions μ_i might live on a non-linear manifold M, they are modeled with an additive predictor η_i living in a linear space by
μ_i = g_p(η_i) = g_p(∑_j h_j(x_i))
where g_p is a response function, which might depend on a pole p \in M
and is typically chosen as g_p = Exp_p, the manifold exponential function
at p. The additive predictor η_i is composed of partial effects
h_j(x_i) as provided by the R packages mboost and FDboost,
but potentially constraining them to a respective linear subspace, e.g.
corresponding to the tangent space at p.
For further details on available covariate effects see
FDboost and the baselearners
help of mboost.
Computationally, it might make a huge difference whether response observations
are measured on a common regular grid or on irregular individual grids. In the
regular case, the linear array model can be utilized
(Brockhaus et al. 2015, Currie et al. 2006) for the design
matrix and the regular structure might also be used to speed up pole and
gradient computation.
This distinction is reflected - and controlled by - the data format and
in particular the format the response is provided in. For a data set with
N observations, data should be
provided as list containing scalar covariate vectors (of length N).
The response should be contained as follows:
in the regular case, the response should be a
tbl_cubewith response values as measures and remaining variables contained inobj.formulaas dimensions, listed according to the covariates.in the irregular case, the response should be a
data.frame(or list) with the response variables appearing in theobj.formula.for backward compatibility, data can also be in the format of
FDboost, i.e.,datais again a list and the response is provided in separate list elements:in the regular case, the response measurements are provided as matrix with N rows corresponding to the observations and the columns containing all measurements in long format and the
dimandobj.formulavariables as vectors along the columns of the matrix.in the irregular case, the columns of the last irregular option above are just separately added to the list.
Value
An object of class mfboost inheriting from FDboost and
mboost.
Brockhaus, S., Scheipl, F., Hothorn, T. and Greven, S. (2015): The functional linear array model. Statistical Modelling, 15(3), 279-300.
Currie, I.D., Durban, M. and Eilers P.H.C. (2006): Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society, Series B-Statistical Methodology, 68(2), 259-280.
See Also
mfFamily,
factorize, data example cells
Examples
# modeling the FORM/SIZE-AND-SHAPE of IRREGULAR curves -------------------
# load irregular cell data
data("cells", package = "manifoldboost")
# subsample (one for each covariate combination)
cellsub <- as.data.frame(cells[-which(names(cells)=="response")])
cellsub$myd <- factor(with(cellsub,
paste0("a=", a, " r=", r, " b=", b, " m=", m)))
subids <- match(unique(cellsub$myd), cellsub$myd)
cellsub <- as.list(cellsub[subids, ])
cellsub$response <- cells$response[as.numeric(cells$response$id) %in% subids, ]
# fit model
cell_model <- mfboost(
formula = response ~ bbsc(a, df = 3, knots = 5) +
bbsc(r, df = 3, knots = 5) +
bbsc(b, df = 3, knots = 5) +
bbsc(m, df = 3, knots = 5),
obj.formula = value^dim ~
bbs(arg, df = 1, differences = 0, knots = 5,
boundary.knots = c(0,1), cyclic = TRUE) | id,
data = cellsub,
family = PlanarSizeShapeL2(
weight_fun = trapez_weights,
arg_range = c(0,1)),
control = boost_control(mstop = 300)
)
# # cross-validation
# set.seed(9382)
# cell_cv <- cvrisk(cell_model,
# folds = cvLong(
# id = cell_model$id,
# weights = cell_model$`(weights)`,
# type = "kfold"),
# grid = 0:mstop(cell_model))
# cell_model[mstop(cell_cv)]
# plot first four predictions
par(mfrow = c(2,2), mar = rep(2, 4) )
plot(cell_model, ids = 1:4, t = "l",
main = cellsub$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("intercept", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# compare with data
plot(cell_model, ids = 1:4, t = "l", y0_ = cell_model$family@mf$y_[1:4],
main = cellsub$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("observation", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# predict dense cells on grids
cellgrid <- cellsub
cellgrid$response <- with(cellgrid$response, expand.grid(
id = unique(id),
arg = seq(0,1, len = 100),
dim = unique(dim),
value = NA))
cellgrid$response$value <- predict(cell_model,
newdata = cellgrid, type = "response")
# factorize effects
cell_fac <- factorize(cell_model)
vimp <- varimp(cell_fac$cov)
plot(vimp, auto.key = FALSE)
# plot two most important effect directions
this <- cell_fac$cov$which(head(names(vimp)[order(vimp, decreasing = TRUE)], 2))
par(mfcol = c(2,2))
plot(cell_fac$resp, which = this, y0_par = list(type="l"))
plot(cell_fac$cov, which = this)
# modeling the SHAPE of REGULAR curves -------------------
# load regular cell data
data("cellr", package = "manifoldboost")
# subsample (one for each covariate combination)
cellsub <- as.data.frame(cellr[-which(names(cellr)=="response")])
cellsub$myd <- factor(with(cellsub,
paste0("a=", a, " r=", r, " b=", b, " m=", m)))
subids <- match(unique(cellsub$myd), cellsub$myd)
cellsub <- as.list(cellsub[subids, ])
cellsub$response <- cellr$response
cellsub$response$dims$id <- ordered(cellsub$response$dims$id[subids],
levels = unique(cellsub$response$dims$id[subids]))
cellsub$response$mets$value <- cellsub$response$mets$value[,,subids]
class(cellsub$response) <- "tbl_cube"
# fit SHAPE model
cell_model <- mfboost(
formula = response ~ bbsc(a, df = 3, knots = 5) +
bbsc(r, df = 3, knots = 5) +
bbsc(b, df = 3, knots = 5) +
bbsc(m, df = 3, knots = 5),
obj.formula = value^dim ~
bbs(arg, df = 1, differences = 0, knots = 5,
boundary.knots = c(0,70), cyclic = TRUE) | id,
data = cellsub,
family = PlanarShapeL2(),
control = boost_control(mstop = 100)
)
# # cross-validation
# set.seed(8768)
# cell_cv <- cvrisk(cell_model,
# folds = cvMa(ydim = cell_model$ydim,
# type = "kfold"),
# grid = 0:mstop(cell_model))
# cell_model[mstop(cell_cv)]
# plot first four predictions
par(mfrow = c(2,2), mar = rep(2, 4) )
plot(cell_model, ids = 1:4, t = "l",
main = cells$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("intercept", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# compare with data
plot(cell_model, ids = 1:4, t = "l", y0_ = cell_model$family@mf$y_[1:4],
main = cellsub$myd[1:4],
seg_par = list(lty = "dashed"))
legend(x = "bottomright", lty = c(1,1, 2),
legend = c("observation", "prediction", "point correspondence"),
col = c("grey", "black", "grey"))
# predict dense cells on grids
cellgrid <- cellsub
cellgrid$response <- cubelyr::tbl_cube(
dimensions = list(
id = cellsub$response$dims$id,
arg = seq(0,70, len = 100),
dim = unique(cellsub$response$dims$dim)
),
measures = list(
value = array(NA, dim = c(29, 100, 2))))
cellgrid$response$mets$value <- array(predict(cell_model,
newdata = cellgrid, type = "response"),
dim = c(29,100,2))
for(i in 1:4)
plot(cellgrid$response$mets$value[i,,], t = "l")
# factorize effects
cell_fac <- factorize(cell_model)
vimp <- varimp(cell_fac$cov)
plot(vimp, auto.key = FALSE)
# plot two most important effect directions
this <- cell_fac$cov$which(head(names(vimp)[order(vimp, decreasing = TRUE)], 2))
par(mfcol = c(2,2))
plot(cell_fac$resp, which = this, y0_par = list(type="l"))
plot(cell_fac$cov, which = this)
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