R/generatePartialDependence.R
In guillermozbta/s2: Machine Learning in R
Defines functions
generatePartialDependenceData
generateFunctionalANOVAData
print.FunctionalANOVAData
doPartialDerivativeIteration
doPartialDependenceIteration
doAggregatePartialDependence
doIndividualPartialDependence
print.PartialDependenceData
plotPartialDependence
plotPartialDependenceGGVIS
Documented in
generateFunctionalANOVAData
generatePartialDependenceData
plotPartialDependence
plotPartialDependenceGGVIS
#' @title Generate partial dependence.
#'
#' @description
#' Estimate how the learned prediction function is affected by one or more features.
#' For a learned function f(x) where x is partitioned into x_s and x_c, the partial dependence of
#' f on x_s can be summarized by averaging over x_c and setting x_s to a range of values of interest,
#' estimating E_(x_c)(f(x_s, x_c)). The conditional expectation of f at observation i is estimated similarly.
#' Additionally, partial derivatives of the marginalized function w.r.t. the features can be computed.
#'
#' @family partial_dependence
#' @family generate_plot_data
#' @aliases PartialDependenceData
#'
#' @param obj [\code{\link{WrappedModel}}]\cr
#' Result of \code{\link{train}}.
#' @param input [\code{data.frame} | \code{\link{Task}}]\cr
#' Input data.
#' @param features [\code{character}]\cr
#' A vector of feature names contained in the training data.
#' If not specified all features in the \code{input} will be used.
#' @param interaction [\code{logical(1)}]\cr
#' Whether the \code{features} should be interacted or not. If \code{TRUE} then the Cartesian product of the
#' prediction grid for each feature is taken, and the partial dependence at each unique combination of
#' values of the features is estimated. Note that if the length of \code{features} is greater than two,
#' \code{\link{plotPartialDependence}} and \code{\link{plotPartialDependenceGGVIS}} cannot be used.
#' If \code{FALSE} each feature is considered separately. In this case \code{features} can be much longer
#' than two.
#' Default is \code{FALSE}.
#' @param derivative [\code{logical(1)}]\cr
#' Whether or not the partial derivative of the learned function with respect to the features should be
#' estimated. If \code{TRUE} \code{interaction} must be \code{FALSE}. The partial derivative of individual
#' observations may be estimated. Note that computation time increases as the learned prediction function
#' is evaluated at \code{gridsize} points * the number of points required to estimate the partial derivative.
#' Additional arguments may be passed to \code{\link[numDeriv]{grad}} (for regression or survival tasks) or
#' \code{\link[numDeriv]{jacobian}} (for classification tasks). Note that functions which are not smooth may
#' result in estimated derivatives of 0 (for points where the function does not change within +/- epsilon)
#' or estimates trending towards +/- infinity (at discontinuities).
#' Default is \code{FALSE}.
#' @param individual [\code{logical(1)}]\cr
#' Whether to plot the individual conditional expectation curves rather than the aggregated curve, i.e.,
#' rather than aggregating (using \code{fun}) the partial dependences of \code{features}, plot the
#' partial dependences of all observations in \code{data} across all values of the \code{features}.
#' The algorithm is developed in Goldstein, Kapelner, Bleich, and Pitkin (2015).
#' Default is \code{FALSE}.
#' @param center [\code{list}]\cr
#' A named list containing the fixed values of the \code{features}
#' used to calculate an individual partial dependence which is then
#' subtracted from each individual partial dependence made across the prediction grid created for the
#' \code{features}: centering the individual partial dependence lines to make them more interpretable.
#' This argument is ignored if \code{individual != TRUE}.
#' Default is \code{NULL}.
#' @param fun [\code{function}]\cr
#' For regression, a function that accepts a numeric vector and returns either a single number
#' such as a measure of location such as the mean, or three numbers, which give a lower bound,
#' a measure of location, and an upper bound. Note if three numbers are returned they must be
#' in this order. For classification with \code{predict.type = "prob"} the function must accept
#' a numeric matrix with the number of columns equal to the number of class levels of the target.
#' For classification with \code{predict.type = "response"} (the default) the function must accept
#' a character vector and output a numeric vector with length equal to the number of classes in the
#' target feature. Two variables, \code{data} and \code{newdata} are made available to \code{fun} internally via a
#' wrapper. `data` is the training data from `input` and `newdata` contains a single point from the
#' prediction grid for \code{features} along with the training data for features not in \code{features}.
#' This allows the computation of weights based on comparisons of the prediction grid to the training data.
#' The default is the mean, unless \code{obj} is classification with \code{predict.type = "response"}
#' in which case the default is the proportion of observations predicted to be in each class.
#' @param bounds [\code{numeric(2)}]\cr
#' The value (lower, upper) the estimated standard error is multiplied by to estimate the bound on a
#' confidence region for a partial dependence. Ignored if \code{predict.type != "se"} for the learner.
#' Default is the 2.5 and 97.5 quantiles (-1.96, 1.96) of the Gaussian distribution.
#' @param resample [\code{character(1)}]\cr
#' Defines how the prediction grid for each feature is created. If \dQuote{bootstrap} then
#' values are sampled with replacement from the training data. If \dQuote{subsample} then
#' values are sampled without replacement from the training data. If \dQuote{none} an evenly spaced
#' grid between either the empirical minimum and maximum, or the minimum and maximum defined by
#' \code{fmin} and \code{fmax}, is created.
#' Default is \dQuote{none}.
#' @param fmin [\code{numeric}]\cr
#' The minimum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = NULL} and when the empirical minimum is higher
#' than the theoretical minimum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical minimum of each numeric feature and NA for factor features.
#' @param fmax [\code{numeric}]\cr
#' The maximum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = "none"} and when the empirical maximum is lower
#' than the theoretical maximum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical maximum of each numeric feature and NA for factor features.
#' @param gridsize [\code{integer(1)}]\cr
#' The length of the prediction grid created for each feature.
#' If \code{resample = "bootstrap"} or \code{resample = "subsample"} then this defines
#' the number of (possibly non-unique) values resampled. If \code{resample = NULL} it defines the
#' length of the evenly spaced grid created.
#' @param range [\code{list}]\cr
#' The range of values of the feature you would want the partial plots on - passed as a numeric list
#' @param ... additional arguments to be passed to \code{\link{predict}}.
#' @return [\code{PartialDependenceData}]. A named list, which contains the partial dependence,
#' input data, target, features, task description, and other arguments controlling the type of
#' partial dependences made.
#'
#' Object members:
#' \item{data}{[\code{data.frame}]\cr
#' Has columns for the prediction: one column for regression and
#' survival analysis, and a column for class and the predicted probability for classification as well
#' as a a column for each element of \code{features}. If \code{individual = TRUE} then there is an
#' additional column \code{idx} which gives the index of the \code{data} that each prediction corresponds to.}
#' \item{task.desc}{[\code{\link{TaskDesc}}]\cr
#' Task description.}
#' \item{target}{Target feature for regression, target feature levels for classification,
#' survival and event indicator for survival.}
#' \item{features}{[\code{character}]\cr
#' Features argument input.}
#' \item{interaction}{[\code{logical(1)}]\cr
#' Whether or not the features were interacted (i.e. conditioning).}
#' \item{derivative}{[\code{logical(1)}]\cr
#' Whether or not the partial derivative was estimated.}
#' \item{individual}{[\code{logical(1)}]\cr
#' Whether the partial dependences were aggregated or the individual curves are retained.}
#' \item{center}{[\code{logical(1)}]\cr
#' If \code{individual == TRUE} whether the partial dependence at the values of the
#' features specified was subtracted from the individual partial dependences. Only displayed if
#' \code{individual == TRUE}.}
#' @references
#' Goldstein, Alex, Adam Kapelner, Justin Bleich, and Emil Pitkin. \dQuote{Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation.} Journal of Computational and Graphical Statistics. Vol. 24, No. 1 (2015): 44-65.
#'
#' Friedman, Jerome. \dQuote{Greedy Function Approximation: A Gradient Boosting Machine.} The Annals of Statistics. Vol. 29. No. 5 (2001): 1189-1232.
#' @examples
#' lrn = makeLearner("regr.svm")
#' fit = train(lrn, bh.task)
#' pd = generatePartialDependenceData(fit, bh.task, "lstat")
#' plotPartialDependence(pd, data = getTaskData(bh.task))
#'
#' lrn = makeLearner("classif.rpart", predict.type = "prob")
#' fit = train(lrn, iris.task)
#' pd = generatePartialDependenceData(fit, iris.task, "Petal.Width")
#' plotPartialDependence(pd, data = getTaskData(iris.task))
#'
#' # simulated example with weights computed via the joint distribution
#' # in practice empirical weights could be constructed by estimating the joint
#' # density from the training data (the data arg to fun) and computing the probability
#' # of the prediction grid under this estimated density (the newdata arg) or
#' # by using something like data depth or outlier classification to weight the
#' # unusualness of points in arg newdata.
#' sigma = matrix(c(1, .5, .5, 1), 2, 2)
#' C = chol(sigma)
#' X = replicate(2, rnorm(100)) %*% C
#' alpha = runif(2, -1, 1)
#' y = X %*% alpha
#' df = data.frame(y, X)
#' tsk = makeRegrTask(data = df, target = "y")
#' fit = train("regr.svm", tsk)
#'
#' w.fun = function(x, newdata) {
#' # compute multivariate normal density given sigma
#' sigma = matrix(c(1, .5, .5, 1), 2, 2)
#' dec = chol(sigma)
#' tmp = backsolve(dec, t(newdata), transpose = TRUE)
#' rss = colSums(tmp^2)
#' logretval = -sum(log(diag(dec))) - 0.5 * ncol(newdata) * log(2 * pi) - 0.5 * rss
#' w = exp(logretval)
#' # weight prediction grid given probability of grid points under the joint
#' # density
#' sum(w * x) / sum(w)
#' }
#'
#' generatePartialDependenceData(fit, tsk, "X1", fun = w.fun)
#' @export
generatePartialDependenceData = function(obj, input, features,
interaction = FALSE, derivative = FALSE, individual = FALSE, center = NULL,
fun = mean, bounds = c(qnorm(.025), qnorm(.975)),
resample = "none", fmin, fmax, gridsize = 10L, range = NULL, ...) {
assertClass(obj, "WrappedModel")
if (obj$learner$predict.type == "se" & individual)
stop("individual = TRUE not compatabile with predict.type = 'se'!")
if (obj$learner$predict.type == "se" & derivative)
stop("derivative = TRUE is not compatible with predict.type = 'se'!")
if (!inherits(input, c("Task", "data.frame")))
stop("input must be a Task or a data.frame!")
if (inherits(input, "Task")) {
data = getTaskData(input)
td = input$task.desc
} else {
data = input
td = obj$task.desc
assertDataFrame(data, col.names = "unique", min.rows = 1L, min.cols = length(obj$features) + length(td$target))
assertSetEqual(colnames(data), c(obj$features, td$target), ordered = FALSE)
}
if (missing(features))
features = colnames(data)[!colnames(data) %in% td$target]
else
assertSubset(features, obj$features)
assertFlag(interaction)
assertFlag(derivative)
if (derivative & interaction)
stop("interaction cannot be TRUE if derivative is TRUE.")
if (derivative) {
if (any(sapply(data[, features, drop = FALSE], class) %in% c("factor", "ordered", "character")))
stop("All features must be numeric to estimate set derivative = TRUE!")
}
assertFlag(individual)
if (individual)
fun = function(x) x
if (!is.null(center)) {
if (derivative)
stop("center cannot be used with derivative = TRUE.")
assertList(center, len = length(features), names = "unique")
if (!all(names(center) %in% features))
stop("The names of the elements in center must be the same as the features.")
center = as.data.frame(do.call("cbind", center))
}
assertFunction(fun)
assertNumeric(bounds, len = 2L)
assertNumber(bounds[1], upper = 0)
assertNumber(bounds[2], lower = 0)
assertChoice(resample, c("none", "bootstrap", "subsample"))
if (missing(fmin))
fmin = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
min(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
if (missing(fmax))
fmax = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
max(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
assertList(fmin, len = length(features))
if (!all(names(fmin) %in% features))
stop("fmin must be a named list with an NA or value corresponding to each feature.")
assertList(fmax, len = length(features))
if (!all(names(fmax) %in% features))
stop("fmax must be a named list with an NA or value corresponding to each feature.")
assertCount(gridsize, positive = TRUE)
if (is.null(range))
rng = generateFeatureGrid(features, data, resample, gridsize, fmin, fmax)
else
rng = range
if (length(features) > 1L & interaction)
rng = expand.grid(rng)
if (td$type == "regr")
target = td$target
else if (td$type == "classif") {
if (length(td$class.levels) > 2L)
target = td$class.levels
else
target = td$positive
} else
target = "Risk"
args = list(obj = obj, data = data, fun = fun, td = td, individual = individual,
bounds = bounds, ...)
if (length(features) > 1L & !interaction) {
out = lapply(features, function(x) {
args$features = x
if (derivative) {
args$bounds = NULL
out = parallelMap(doPartialDerivativeIteration, x = rng[[x]], more.args = args)
rng = as.data.frame(rng[[x]])
colnames(rng) = x
centerpred = NULL
} else {
rng = as.data.frame(rng[[x]])
colnames(rng) = x
args$rng = rng
out = parallelMap(doPartialDependenceIteration, i = seq_len(nrow(rng)), more.args = args)
if (!is.null(center) & individual)
centerpred = as.data.frame(doPartialDependenceIteration(obj, data, center[, x, drop = FALSE],
x, fun, td, 1, bounds = bounds, ...))
else
centerpred = NULL
}
if (!individual)
doAggregatePartialDependence(out, td, target, x, rng)
else
doIndividualPartialDependence(out, td, nrow(data), rng, target, x, centerpred)
})
out = setDF(rbindlist(out, fill = TRUE))
} else {
args$features = features
if (derivative) {
args$bounds = NULL
out = parallelMap(doPartialDerivativeIteration, x = rng[[features]], more.args = args)
centerpred = NULL
rng = as.data.frame(rng)
colnames(rng) = features
} else {
rng = as.data.frame(rng)
colnames(rng) = features
args$rng = rng
out = parallelMap(doPartialDependenceIteration, i = seq_len(nrow(rng)), more.args = args)
if (!is.null(center) & individual)
centerpred = as.data.frame(doPartialDependenceIteration(obj, data, center, features, fun, td, 1, bounds))
else
centerpred = NULL
}
if (!individual)
out = doAggregatePartialDependence(out, td, target, features, rng)
else
out = doIndividualPartialDependence(out, td, nrow(data), rng, target, features, centerpred)
}
if (td$type %in% c("regr", "surv"))
out = out[, c(target, features, colnames(out)[!colnames(out) %in% c(target, features)])]
else
out = out[, c("Class", "Probability", features,
colnames(out)[!colnames(out) %in% c("Class", "Probability", features)])]
makeS3Obj("PartialDependenceData",
data = out,
task.desc = td,
target = target,
features = features,
interaction = interaction,
derivative = derivative,
individual = individual,
center = !is.null(center))
}
#' @title Generate a functional ANOVA decomposition
#'
#' @description
#' Decompose a learned prediction function as a sum of components estimated via partial dependence.
#'
#' @family partial_dependence functional_anova
#' @family generate_plot_data
#' @aliases FunctionalANOVAData
#'
#' @param obj [\code{\link{WrappedModel}}]\cr
#' Result of \code{\link{train}}.
#' @param input [\code{data.frame} | \code{\link{Task}}]\cr
#' Input data.
#' @param features [\code{character}]\cr
#' A vector of feature names contained in the training data.
#' If not specified all features in the \code{input} will be used.
#' @param depth [\code{integer(1)}]\cr
#' An integer indicating the depth of interaction amongst the features to compute. Default 1.
#' @param fun [\code{function}]\cr
#' A function that accepts a numeric vector and returns either a single number
#' such as a measure of location such as the mean, or three numbers, which give a lower bound,
#' a measure of location, and an upper bound. Note if three numbers are returned they must be
#' in this order. Two variables, \code{data} and \code{newdata} are made available to \code{fun} internally via a
#' wrapper. `data` is the training data from `input` and `newdata` contains a single point from the
#' prediction grid for \code{features} along with the training data for features not in \code{features}.
#' This allows the computation of weights based on comparisons of the prediction grid to the training data.
#' The default is the mean.
#' @param bounds [\code{numeric(2)}]\cr
#' The value (lower, upper) the estimated standard error is multiplied by to estimate the bound on a
#' confidence region for a partial dependence. Ignored if \code{predict.type != "se"} for the learner.
#' Default is the 2.5 and 97.5 quantiles (-1.96, 1.96) of the Gaussian distribution.
#' @param resample [\code{character(1)}]\cr
#' Defines how the prediction grid for each feature is created. If \dQuote{bootstrap} then
#' values are sampled with replacement from the training data. If \dQuote{subsample} then
#' values are sampled without replacement from the training data. If \dQuote{none} an evenly spaced
#' grid between either the empirical minimum and maximum, or the minimum and maximum defined by
#' \code{fmin} and \code{fmax}, is created.
#' Default is \dQuote{none}.
#' @param fmin [\code{numeric}]\cr
#' The minimum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = NULL} and when the empirical minimum is higher
#' than the theoretical minimum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical minimum of each numeric feature and NA for factor features.
#' @param fmax [\code{numeric}]\cr
#' The maximum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = "none"} and when the empirical maximum is lower
#' than the theoretical maximum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical maximum of each numeric feature and NA for factor features.
#' @param gridsize [\code{integer(1)}]\cr
#' The length of the prediction grid created for each feature.
#' If \code{resample = "bootstrap"} or \code{resample = "subsample"} then this defines
#' the number of (possibly non-unique) values resampled. If \code{resample = NULL} it defines the
#' length of the evenly spaced grid created. Default 10.
#' @param ... additional arguments to be passed to \code{\link{predict}}.
#' @return [\code{FunctionalANOVAData}]. A named list, which contains the computed effects of the specified
#' depth amongst the features.
#'
#' Object members:
#' \item{data}{[\code{data.frame}]\cr
#' Has columns for the prediction: one column for regression and an additional two if bounds are used.
#' The \dQuote{effect} column specifies which features the prediction corresponds to.}
#' \item{task.desc}{[\code{\link{TaskDesc}}]\cr
#' Task description.}
#' \item{target}{The target feature for regression.}
#' \item{features}{[\code{character}]\cr
#' Features argument input.}
#' \item{interaction}{[\code{logical(1)}]\cr
#' Whether or not the \code{depth} is greater than 1.}
#' @references
#' Giles Hooker, \dQuote{Discovering additive structure in black box functions.} Proceedings of the 10th ACM SIGKDD international conference on Knowledge discovery and data mining (2004): 575-580.
#' @examples
#' fit = train("regr.rpart", bh.task)
#' fa = generateFunctionalANOVAData(fit, bh.task, c("lstat", "crim"), depth = 2L)
#' plotPartialDependence(fa)
#' @export
generateFunctionalANOVAData = function(obj, input, features, depth = 1L, fun = mean,
bounds = c(qnorm(.025), qnorm(.975)),
resample = "none", fmin, fmax, gridsize = 10L, ...) {
assertClass(obj, "WrappedModel")
if (!inherits(input, c("Task", "data.frame")))
stop("input must be a Task or a data.frame!")
if (inherits(input, "Task")) {
data = getTaskData(input)
td = input$task.desc
} else {
data = input
td = obj$task.desc
assertDataFrame(data, col.names = "unique", min.rows = 1L, min.cols = length(obj$features) + length(td$target))
assertSetEqual(colnames(data), c(obj$features, td$target), ordered = FALSE)
}
if (!td$type == "regr")
stop("only regression tasks are permitted")
excluded = colnames(data)
excluded = excluded[!excluded %in% c(features, td$target)]
assertChoice(resample, c("none", "bootstrap", "subsample"))
if (missing(fmin))
fmin = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
min(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
if (missing(fmax))
fmax = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
max(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
assertList(fmin, len = length(features))
if (!all(names(fmin) %in% features))
stop("fmin must be a named list with an NA or value corresponding to each feature.")
assertList(fmax, len = length(features))
if (!all(names(fmax) %in% features))
stop("fmax must be a named list with an NA or value corresponding to each feature.")
assertCount(gridsize, positive = TRUE)
assertIntegerish(depth, lower = 1L, upper = length(features), len = 1L)
assertFunction(fun)
assertNumeric(bounds, len = 2L)
assertNumber(bounds[1], upper = 0)
assertNumber(bounds[2], lower = 0)
## generate grid
fixed = generateFeatureGrid(features, data, resample, gridsize, fmin, fmax)
## generate list of effects to evaluate and associate with grid
U = unlist(lapply(1:depth, function(x) combn(features, x, simplify = FALSE)), recursive = FALSE)
depths = sapply(U, length)
effects = sapply(U, function(u) stri_paste(u, collapse = ":"))
fixed.grid = lapply(U, function(u) expand.grid(fixed[u]))
names(fixed.grid) = effects
target = td$target
## generate each effect
pd = lapply(U, function(u, args) {
args$features = u
args$rng = fixed.grid[[stri_paste(u, collapse = ":")]]
out = parallelMap(doPartialDependenceIteration, i = seq_len(nrow(args$rng)), more.args = args)
doAggregatePartialDependence(out, td, target, u, args$rng)
}, args = list(obj = obj, data = data, fun = fun, td = td, bounds = bounds, ...))
names(pd) = effects
if (all(c("upper", "lower") %in% colnames(pd[[1]])) |
obj$learner$predict.type == "se")
target = c("upper", "lower", target)
## remove lower order effects
f = lapply(U, function(u) {
hoe = pd[[stri_paste(u, collapse = ":")]]
if (length(u) > 1) {
sub = combn(u, length(u) - 1, simplify = FALSE)
loe = lapply(pd[unlist(sub)], function(x) {
to.match = colnames(x)[!(colnames(x) %in% target)]
out = merge(x, hoe[, to.match, drop = FALSE], by = to.match)
out[, colnames(out) %in% target]
})
hoe[, target] = hoe[, target] - Reduce("+", loe)
}
hoe
})
names(f) = effects
makeS3Obj(c("FunctionalANOVAData", "PartialDependenceData"),
data = setDF(rbindlist(f[depths == depth], fill = TRUE, idcol = "effect")),
task.desc = td,
target = target[!target %in% c("upper", "lower")],
features = features,
interaction = depth > 1L,
derivative = FALSE,
individual = FALSE,
center = FALSE)
}
#' @export
print.FunctionalANOVAData = function(x, ...) {
catf("FunctionalANOVAData")
catf("Task: %s", x$task.desc$id)
catf("Features: %s", stri_paste(x$features, collapse = ", "))
catf("Target: %s", stri_paste(x$target, collapse = ", "))
catf("Interaction Depth: %s", x$depth)
catf("Effects Computed: %s", stri_paste(levels(x$data$effect), collapse = ", "))
printHead(x$data, ...)
}
doPartialDerivativeIteration = function(x, obj, data, features, fun, td, individual, ...) {
fun.wrapper = function(x, newdata, data, ...) {
args = formals(fun)
if (all(c("newdata", "data") %in% names(args))) {
fun(x, newdata = newdata, data = data, ...)
} else if ("newdata" %in% names(args)) {
fun(x, newdata = newdata, ...)
} else if ("data" %in% names(args)) {
fun(x, data = data, ...)
} else {
fun(x, ...)
}
}
f = function(x, obj, data, features, fun, td, ...) {
newdata = data
newdata[features] = x
pred = do.call("predict", c(list("object" = obj, "newdata" = newdata), list(...)))
if (obj$learner$predict.type == "response")
fun(getPredictionResponse(pred), ...)
else if (length(obj$task.desc$class.levels) == 2L)
fun(getPredictionProbabilities(pred), ...)
else
apply(getPredictionProbabilities(pred), 2, fun, ...)
}
if (!individual) {
# construct function appropriate for numDeriv w/ aggregate predictions
if (obj$learner$predict.type == "response")
numDeriv::grad(func = f, x = x, obj = obj, data = data, features = features, fun = fun.wrapper, td = td, ...)
else
t(numDeriv::jacobian(func = f, x = x, obj = obj, data = data, features = features, fun = fun.wrapper, td = td, ...))
} else {
if (obj$learner$predict.type == "response")
sapply(seq_len(nrow(data)), function(idx)
numDeriv::grad(func = f, x = x, obj = obj, data = data[idx, , drop = FALSE],
features = features, fun = fun.wrapper, td = td, ...))
else
t(sapply(seq_len(nrow(data)), function(idx) numDeriv::jacobian(func = f, x = x, obj = obj,
data = data[idx, , drop = FALSE], features = features, fun = fun.wrapper, td = td, ...)))
}
}
doPartialDependenceIteration = function(obj, data, rng, features, fun, td, i, bounds, individual = FALSE, ...) {
newdata = data
newdata[features] = rng[i, ]
fun.wrapper = function(x, newdata, data, ...) {
args = formals(fun)
if (all(c("newdata", "data") %in% names(args))) {
fun(x, newdata = newdata, data = data, ...)
} else if ("newdata" %in% names(args)) {
fun(x, newdata = newdata, ...)
} else if ("data" %in% names(args)) {
fun(x, data = data, ...)
} else {
fun(x, ...)
}
}
pred = do.call("predict", c(list("object" = obj, "newdata" = newdata), list(...)))
if (obj$learner$predict.type == "response") {
fun.wrapper(getPredictionResponse(pred), newdata, data, ...)
} else if (length(obj$task.desc$class.levels) == 2L) {
fun.wrapper(getPredictionProbabilities(pred), newdata, data, ...)
} else if (obj$learner$predict.type == "se") {
point = getPredictionResponse(pred)
out = cbind(point + outer(getPredictionSE(pred), bounds), point)[, c(1, 3, 2)]
unname(apply(out, 2, fun.wrapper, newdata = newdata, data = data, ...))
} else {
apply(getPredictionProbabilities(pred), 2, fun.wrapper, newdata = newdata,
data = data, ...)
}
}
doAggregatePartialDependence = function(out, td, target, features, rng) {
out = as.data.frame(do.call("rbind", out))
if (td$type == "regr" & ncol(out) == 3L)
colnames(out) = c("lower", target, "upper")
else
colnames(out) = target
out = cbind(out, rng)
if (td$type == "regr" & all(c("upper", "lower", target) %in% colnames(out)))
if (!all(out$lower <= out[[target]] & out[[target]] <= out$upper))
stop("function argument must return a sorted numeric vector ordered lowest to highest.")
if (all(target %in% td$class.levels)) {
out = melt(out, id.vars = features, variable = "Class", value.name = "Probability", variable.factor = TRUE)
out$Class = stri_replace_all(out$Class, "", regex = "^prob\\.")
}
out
}
doIndividualPartialDependence = function(out, td, n, rng, target, features, centerpred = NULL) {
if (td$type == "classif" & length(td$class.levels) > 2L) {
if (!is.null(centerpred))
out = lapply(out, function(x) x - centerpred) else
out = lapply(out, as.data.frame)
out = as.data.frame(rbindlist(out))
colnames(out) = target
idx = rep(seq_len(n), nrow(rng))
rng = rng[rep(seq_len(nrow(rng)), each = n), , drop = FALSE]
out = cbind(out, rng, idx, row.names = NULL)
out = melt(out, id.vars = c(features, "idx"),
variable.name = "Class", value.name = "Probability", variable.factor = TRUE)
out$idx = interaction(out$idx, out$Class)
} else {
out = as.data.frame(setDT(transpose(out))) # see https://github.com/Rdatatable/data.table/issues/600
if (!is.null(centerpred))
out = out - setDF(transpose(rep(centerpred, nrow(out)))) #t(as.data.frame(lapply(out, function(x) unname(x - centerpred))))
colnames(out) = 1:n
out = cbind(out, rng)
out = melt(out, id.vars = features, variable.name = "idx", value.name = target)
if (td$type == "classif")
out = melt(out, id.vars = c(features, "idx"), value.name = "Probability",
variable.name = "Class", variable.factor = TRUE)
}
out
}
#' @export
print.PartialDependenceData = function(x, ...) {
catf("PartialDependenceData")
catf("Task: %s", x$task.desc$id)
catf("Features: %s", stri_paste(x$features, collapse = ", ", sep = " "))
catf("Target: %s", stri_paste(x$target, collapse = ", ", sep = " "))
catf("Derivative: %s", x$derivative)
catf("Interaction: %s", x$interaction)
catf("Individual: %s", x$individual)
if (x$individual)
catf("Predictions centered: %s", x$center)
printHead(x$data, ...)
}
#' @title Plot a partial dependence with ggplot2.
#' @description
#' Plot a partial dependence from \code{\link{generatePartialDependenceData}} using ggplot2.
#'
#' @family partial_dependence
#' @family plot
#'
#' @param obj [\code{PartialDependenceData}]\cr
#' Generated by \code{\link{generatePartialDependenceData}}.
#' @param geom [\code{charater(1)}]\cr
#' The type of geom to use to display the data. Can be \dQuote{line} or \dQuote{tile}.
#' For tiling at least two features must be used with \code{interaction = TRUE} in the call to
#' \code{\link{generatePartialDependenceData}}. This may be used in conjuction with the
#' \code{facet} argument if three features are specified in the call to
#' \code{\link{generatePartialDependenceData}}.
#' Default is \dQuote{line}.
#' @param facet [\code{character(1)}]\cr
#' The name of a feature to be used for facetting.
#' This feature must have been an element of the \code{features} argument to
#' \code{\link{generatePartialDependenceData}} and is only applicable when said argument had length
#' greater than 1.
#' The feature must be a factor or an integer.
#' If \code{\link{generatePartialDependenceData}} is called with the \code{interaction} argument \code{FALSE}
#' (the default) with argument \code{features} of length greater than one, then \code{facet} is ignored and
#' each feature is plotted in its own facet.
#' Default is \code{NULL}.
#' @template arg_facet_nrow_ncol
#' @param p [\code{numeric(1)}]\cr
#' If \code{individual = TRUE} then \code{sample} allows the user to sample without replacement
#' from the output to make the display more readable. Each row is sampled with probability \code{p}.
#' Default is \code{1}.
#' @param data [\code{data.frame}]\cr
#' Data points to plot. Usually the training data. For survival and binary classification tasks a rug plot
#' wherein ticks represent failures or instances of the positive class are shown. For regression tasks
#' points are shown. For multiclass classification tasks ticks are shown and colored according to their class.
#' Both the features and the target must be included.
#' Default is \code{NULL}.
#' @template ret_gg2
#' @export
plotPartialDependence = function(obj, geom = "line", facet = NULL, facet.wrap.nrow = NULL,
facet.wrap.ncol = NULL, p = 1, data = NULL) {
assertClass(obj, "PartialDependenceData")
assertChoice(geom, c("tile", "line"))
if (obj$interaction & length(obj$features) > 2L & geom != "tile")
stop("Cannot plot more than 2 features together with line plots.")
if (geom == "tile") {
if (!obj$interaction)
stop("obj argument created by generatePartialDependenceData was called with interaction = FALSE!")
}
if ("FunctionalANOVAData" %in% class(obj)) {
if (length(unique(obj$data$effect)) > 1L & obj$interaction)
stop("Cannot plot multiple ANOVA effects of depth > 1.")
}
if (!is.null(data)) {
assertDataFrame(data, col.names = "unique", min.rows = 1L,
min.cols = length(obj$features) + length(obj$td$target))
assertSubset(obj$features, colnames(data), empty.ok = FALSE)
}
if (!is.null(facet)) {
assertChoice(facet, obj$features)
if (!length(obj$features) %in% 2:3)
stop("obj argument created by generatePartialDependenceData must be called with two or three features to use this argument!")
if (!obj$interaction)
stop("obj argument created by generatePartialDependenceData must be called with interaction = TRUE to use this argument!")
features = obj$features[which(obj$features != facet)]
if (is.factor(obj$data[[facet]])) {
obj$data[[facet]] = stri_paste(facet, "=", obj$data[[facet]], sep = " ")
} else if (is.character(obj$data[[facet]])) {
obj$data[[facet]] = stri_paste(facet, "=", as.factor(obj$data[[facet]]), sep = " ")
} else if (is.numeric(obj$data[[facet]])) {
obj$data[[facet]] = stri_paste(facet, "=", as.factor(signif(obj$data[[facet]], 3L)), sep = " ")
} else {
stop("Invalid input to facet arg. Must refer to a numeric/integer, character, or facet feature.")
}
scales = "fixed"
} else {
features = obj$features
if (length(features) > 1L & !(length(features) == 2L & geom == "tile")) {
facet = "Feature"
scales = "free_x"
}
}
if (p != 1) {
assertNumber(p, lower = 0, upper = 1, finite = TRUE)
if (!obj$individual)
stop("obj argument created by generatePartialDependenceData must be called with individual = TRUE to use this argument!")
rows = unique(obj$data$idx)
id = sample(rows, size = floor(p * length(rows)))
obj$data = obj$data[which(obj$data$idx %in% id), ]
}
if (obj$task.desc$type %in% c("regr", "classif"))
target = obj$task.desc$target
else
target = "Risk"
bounds = all(c("lower", "upper") %in% colnames(obj$data) & obj$task.desc$type %in% c("surv", "regr") &
length(features) < 3L & geom == "line")
if (geom == "line") {
idx = which(sapply(obj$data, class) == "factor" & colnames(obj$data) %in% features)
# explicit casting previously done implicitly by reshape2::melt.data.frame
for (id in idx) obj$data[, id] = as.numeric(obj$data[, id])
obj$data = setDF(melt(data.table(obj$data),
id.vars = colnames(obj$data)[!colnames(obj$data) %in% features],
variable = "Feature", value.name = "Value", na.rm = TRUE, variable.factor = TRUE))
if (!obj$individual) {
if (obj$task.desc$type %in% c("regr", "surv"))
plt = ggplot(obj$data, aes_string("Value", target)) +
geom_line(color = ifelse(is.null(data), "black", "red")) + geom_point()
else
plt = ggplot(obj$data, aes_string("Value", "Probability", group = "Class", color = "Class")) +
geom_line() + geom_point()
} else {
if (obj$task.desc$type %in% c("regr", "surv")) {
plt = ggplot(obj$data, aes_string("Value", target, group = "idx")) +
geom_line(alpha = .25, color = ifelse(is.null(data), "black", "red")) + geom_point()
} else {
plt = ggplot(obj$data, aes_string("Value", "Probability", group = "idx", color = "Class")) +
geom_line(alpha = .25) + geom_point()
}
}
if (length(features) == 1L) {
if (obj$task.desc$type %in% c("regr", "surv"))
plt = plt + labs(x = features, y = target)
else
plt = plt + labs(x = features)
}
# bounds from fun or se estimation
if (bounds)
plt = plt + geom_ribbon(aes_string(ymin = "lower", ymax = "upper"), alpha = .5)
# labels for ice plots
if (obj$center)
plt = plt + ylab(stri_paste(target, "(centered)", sep = " "))
if (obj$derivative)
plt = plt + ylab(stri_paste(target, "(derivative)", sep = " "))
} else { ## tiling
if (obj$task.desc$type == "classif") {
target = "Probability"
facet = "Class"
scales = "free"
}
plt = ggplot(obj$data, aes_string(x = features[1], y = features[2], fill = target))
plt = plt + geom_raster(aes_string(fill = target))
# labels for ICE plots
if (obj$center)
plt = plt + scale_fill_continuous(guide = guide_colorbar(title = stri_paste(target, "(centered)", sep = " ")))
if (obj$derivative)
plt = plt + scale_fill_continuous(guide = guide_colorbar(title = stri_paste(target, "(derivative)", sep = " ")))
}
# facetting
if (!is.null(facet)) {
plt = plt + facet_wrap(as.formula(stri_paste("~", facet)), scales = scales,
nrow = facet.wrap.nrow, ncol = facet.wrap.ncol)
}
# data overplotting
if (!is.null(data)) {
data = data[, colnames(data) %in% c(obj$features, obj$task.desc$target)]
if (!is.null(facet)) {
if (!facet %in% obj$features)
data = melt(data, id.vars = c(obj$task.desc$target, obj$features[obj$features == facet]),
variable = "Feature", value.name = "Value", na.rm = TRUE, variable.factor = TRUE)
if (facet %in% obj$features) {
if (!is.factor(data[[facet]]))
data[[facet]] = stri_paste(facet, "=", as.factor(signif(data[[facet]], 2)), sep = " ")
else
data[[facet]] = stri_paste(facet, "=", data[[facet]], sep = " ")
}
}
if (geom == "line") {
if (obj$task.desc$type %in% c("classif", "surv")) {
if (obj$task.desc$type == "classif") {
if (!is.na(obj$task.desc$positive)) {
plt = plt + geom_rug(aes_string(plt$labels$x, color = obj$task.desc$target),
data[data[[obj$task.desc$target]] == obj$task.desc$positive, ],
alpha = .25, inherit.aes = FALSE)
} else {
plt = plt + geom_rug(aes_string(plt$labels$x), data, alpha = .25, inherit.aes = FALSE)
}
} else {
plt = plt + geom_rug(aes_string(plt$labels$x),
data[data[[obj$task.desc$target[2]]], ],
alpha = .25, inherit.aes = FALSE)
}
} else {
plt = plt + geom_point(aes_string(plt$labels$x, obj$task.desc$target),
data, alpha = .25, inherit.aes = FALSE)
}
} else {
plt = plt + geom_point(aes_string(plt$labels$x, plt$labels$y), data, alpha = .25, inherit.aes = FALSE)
}
}
plt
}
#' @title Plot a partial dependence using ggvis.
#' @description
#' Plot partial dependence from \code{\link{generatePartialDependenceData}} using ggvis.
#'
#' @family partial_dependence
#' @family plot
#'
#' @param obj [\code{PartialDependenceData}]\cr
#' Generated by \code{\link{generatePartialDependenceData}}.
#' @param interact [\code{character(1)}]\cr
#' The name of a feature to be mapped to an interactive sidebar using Shiny.
#' This feature must have been an element of the \code{features} argument to
#' \code{\link{generatePartialDependenceData}} and is only applicable when said argument had length
#' greater than 1.
#' If \code{\link{generatePartialDependenceData}} is called with the \code{interaction} argument \code{FALSE}
#' (the default) with argument \code{features} of length greater than one, then \code{interact} is ignored and
#' the feature displayed is controlled by an interactive side panel.
#' Default is \code{NULL}.
#' @param p [\code{numeric(1)}]\cr
#' If \code{individual = TRUE} then \code{sample} allows the user to sample without replacement
#' from the output to make the display more readable. Each row is sampled with probability \code{p}.
#' Default is \code{1}.
#' @template ret_ggv
#' @export
plotPartialDependenceGGVIS = function(obj, interact = NULL, p = 1) {
requirePackages("_ggvis")
assertClass(obj, "PartialDependenceData")
if (!is.null(interact))
assertChoice(interact, obj$features)
if (obj$interaction & length(obj$features) > 2L)
stop("It is only possible to plot 2 features with this function.")
if (!obj$interaction & !is.null(interact))
stop("obj argument created by generatePartialDependenceData was called with interaction = FALSE!")
if (p != 1) {
assertNumber(p, lower = 0, upper = 1, finite = TRUE)
if (!obj$individual)
stop("obj argument created by generatePartialDependenceData must be called with individual = TRUE to use this argument!")
rows = unique(obj$data$idx)
id = sample(rows, size = floor(p * length(rows)))
obj$data = obj$data[which(obj$data$idx %in% id), ]
}
if (obj$interaction & length(obj$features) == 2L) {
if (is.null(interact))
interact = obj$features[-which.max(sapply(obj$features, function(x) length(unique(obj$data[[x]]))))]
x = obj$features[which(obj$features != interact)]
if (is.factor(obj$data[[interact]]))
choices = levels(obj$data[[interact]])
else
choices = sort(unique(obj$data[[interact]]))
} else if (!obj$interaction & length(obj$features) > 1L) {
id = colnames(obj$data)[!colnames(obj$data) %in% obj$features]
obj$data = melt(obj$data, id.vars = id, variable.name = "Feature",
value.name = "Value", na.rm = TRUE, variable.factor = TRUE)
interact = "Feature"
choices = obj$features
} else
interact = NULL
bounds = all(c("lower", "upper") %in% colnames(obj$data) & obj$task.desc$type %in% c("surv", "regr"))
if (obj$task.desc$type %in% c("regr", "classif"))
target = obj$task.desc$target
else
target = "Risk"
createPlot = function(td, target, interaction, individual, data, x, bounds) {
classif = td$type == "classif" & all(target %in% td$class.levels)
if (classif) {
if (interaction)
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name("Probability")),
ggvis::prop("stroke", as.name("Class")))
else if (!interaction & !is.null(interact)) ## no interaction but multiple features
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name("Value")),
ggvis::prop("y", as.name("Probability")),
ggvis::prop("stroke", as.name("Class")))
else
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name("Probability")),
ggvis::prop("stroke", as.name("Class")))
} else { ## regression/survival
if (interaction)
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name(target)))
else if (!interaction & !is.null(interact))
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name("Value")),
ggvis::prop("y", as.name(target)))
else
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name(target)))
}
if (bounds)
plt = ggvis::layer_ribbons(plt,
ggvis::prop("y", as.name("lower")),
ggvis::prop("y2", as.name("upper")),
ggvis::prop("opacity", .5))
if (individual) {
plt = ggvis::group_by_.ggvis(plt, as.name("idx"))
plt = ggvis::layer_paths(plt, ggvis::prop("opacity", .25))
} else {
if (classif)
plt = ggvis::layer_points(plt, ggvis::prop("fill", as.name("Class")))
else
plt = ggvis::layer_points(plt)
plt = ggvis::layer_lines(plt)
}
plt
}
if (obj$center)
header = stri_paste(target, "(centered)", sep = " ")
else if (obj$derivative)
header = stri_paste(target, "(derivative)", sep = " ")
else
header = target
if (!is.null(interact)) {
requirePackages("_shiny")
panel = shiny::selectInput("interaction_select", interact, choices)
ui = shiny::shinyUI(
shiny::pageWithSidebar(
shiny::headerPanel(header),
shiny::sidebarPanel(panel),
shiny::mainPanel(
shiny::uiOutput("ggvis_ui"),
ggvis::ggvisOutput("ggvis")
)
))
server = shiny::shinyServer(function(input, output) {
plt = shiny::reactive(createPlot(obj$task.desc, obj$target, obj$interaction, obj$individual,
obj$data[obj$data[[interact]] == input$interaction_select, ],
x, bounds))
ggvis::bind_shiny(plt, "ggvis", "ggvis_ui")
})
shiny::shinyApp(ui, server)
} else
createPlot(obj$task.desc, obj$target, obj$interaction, obj$individual, obj$data, obj$features, bounds)
}
guillermozbta/s2 documentation built on May 17, 2019, 4:01 p.m.
R Package Documentation
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Defines functions generatePartialDependenceData generateFunctionalANOVAData print.FunctionalANOVAData doPartialDerivativeIteration doPartialDependenceIteration doAggregatePartialDependence doIndividualPartialDependence print.PartialDependenceData plotPartialDependence plotPartialDependenceGGVIS
Documented in generateFunctionalANOVAData generatePartialDependenceData plotPartialDependence plotPartialDependenceGGVIS
#' @title Generate partial dependence.
#'
#' @description
#' Estimate how the learned prediction function is affected by one or more features.
#' For a learned function f(x) where x is partitioned into x_s and x_c, the partial dependence of
#' f on x_s can be summarized by averaging over x_c and setting x_s to a range of values of interest,
#' estimating E_(x_c)(f(x_s, x_c)). The conditional expectation of f at observation i is estimated similarly.
#' Additionally, partial derivatives of the marginalized function w.r.t. the features can be computed.
#'
#' @family partial_dependence
#' @family generate_plot_data
#' @aliases PartialDependenceData
#'
#' @param obj [\code{\link{WrappedModel}}]\cr
#' Result of \code{\link{train}}.
#' @param input [\code{data.frame} | \code{\link{Task}}]\cr
#' Input data.
#' @param features [\code{character}]\cr
#' A vector of feature names contained in the training data.
#' If not specified all features in the \code{input} will be used.
#' @param interaction [\code{logical(1)}]\cr
#' Whether the \code{features} should be interacted or not. If \code{TRUE} then the Cartesian product of the
#' prediction grid for each feature is taken, and the partial dependence at each unique combination of
#' values of the features is estimated. Note that if the length of \code{features} is greater than two,
#' \code{\link{plotPartialDependence}} and \code{\link{plotPartialDependenceGGVIS}} cannot be used.
#' If \code{FALSE} each feature is considered separately. In this case \code{features} can be much longer
#' than two.
#' Default is \code{FALSE}.
#' @param derivative [\code{logical(1)}]\cr
#' Whether or not the partial derivative of the learned function with respect to the features should be
#' estimated. If \code{TRUE} \code{interaction} must be \code{FALSE}. The partial derivative of individual
#' observations may be estimated. Note that computation time increases as the learned prediction function
#' is evaluated at \code{gridsize} points * the number of points required to estimate the partial derivative.
#' Additional arguments may be passed to \code{\link[numDeriv]{grad}} (for regression or survival tasks) or
#' \code{\link[numDeriv]{jacobian}} (for classification tasks). Note that functions which are not smooth may
#' result in estimated derivatives of 0 (for points where the function does not change within +/- epsilon)
#' or estimates trending towards +/- infinity (at discontinuities).
#' Default is \code{FALSE}.
#' @param individual [\code{logical(1)}]\cr
#' Whether to plot the individual conditional expectation curves rather than the aggregated curve, i.e.,
#' rather than aggregating (using \code{fun}) the partial dependences of \code{features}, plot the
#' partial dependences of all observations in \code{data} across all values of the \code{features}.
#' The algorithm is developed in Goldstein, Kapelner, Bleich, and Pitkin (2015).
#' Default is \code{FALSE}.
#' @param center [\code{list}]\cr
#' A named list containing the fixed values of the \code{features}
#' used to calculate an individual partial dependence which is then
#' subtracted from each individual partial dependence made across the prediction grid created for the
#' \code{features}: centering the individual partial dependence lines to make them more interpretable.
#' This argument is ignored if \code{individual != TRUE}.
#' Default is \code{NULL}.
#' @param fun [\code{function}]\cr
#' For regression, a function that accepts a numeric vector and returns either a single number
#' such as a measure of location such as the mean, or three numbers, which give a lower bound,
#' a measure of location, and an upper bound. Note if three numbers are returned they must be
#' in this order. For classification with \code{predict.type = "prob"} the function must accept
#' a numeric matrix with the number of columns equal to the number of class levels of the target.
#' For classification with \code{predict.type = "response"} (the default) the function must accept
#' a character vector and output a numeric vector with length equal to the number of classes in the
#' target feature. Two variables, \code{data} and \code{newdata} are made available to \code{fun} internally via a
#' wrapper. `data` is the training data from `input` and `newdata` contains a single point from the
#' prediction grid for \code{features} along with the training data for features not in \code{features}.
#' This allows the computation of weights based on comparisons of the prediction grid to the training data.
#' The default is the mean, unless \code{obj} is classification with \code{predict.type = "response"}
#' in which case the default is the proportion of observations predicted to be in each class.
#' @param bounds [\code{numeric(2)}]\cr
#' The value (lower, upper) the estimated standard error is multiplied by to estimate the bound on a
#' confidence region for a partial dependence. Ignored if \code{predict.type != "se"} for the learner.
#' Default is the 2.5 and 97.5 quantiles (-1.96, 1.96) of the Gaussian distribution.
#' @param resample [\code{character(1)}]\cr
#' Defines how the prediction grid for each feature is created. If \dQuote{bootstrap} then
#' values are sampled with replacement from the training data. If \dQuote{subsample} then
#' values are sampled without replacement from the training data. If \dQuote{none} an evenly spaced
#' grid between either the empirical minimum and maximum, or the minimum and maximum defined by
#' \code{fmin} and \code{fmax}, is created.
#' Default is \dQuote{none}.
#' @param fmin [\code{numeric}]\cr
#' The minimum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = NULL} and when the empirical minimum is higher
#' than the theoretical minimum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical minimum of each numeric feature and NA for factor features.
#' @param fmax [\code{numeric}]\cr
#' The maximum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = "none"} and when the empirical maximum is lower
#' than the theoretical maximum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical maximum of each numeric feature and NA for factor features.
#' @param gridsize [\code{integer(1)}]\cr
#' The length of the prediction grid created for each feature.
#' If \code{resample = "bootstrap"} or \code{resample = "subsample"} then this defines
#' the number of (possibly non-unique) values resampled. If \code{resample = NULL} it defines the
#' length of the evenly spaced grid created.
#' @param range [\code{list}]\cr
#' The range of values of the feature you would want the partial plots on - passed as a numeric list
#' @param ... additional arguments to be passed to \code{\link{predict}}.
#' @return [\code{PartialDependenceData}]. A named list, which contains the partial dependence,
#' input data, target, features, task description, and other arguments controlling the type of
#' partial dependences made.
#'
#' Object members:
#' \item{data}{[\code{data.frame}]\cr
#' Has columns for the prediction: one column for regression and
#' survival analysis, and a column for class and the predicted probability for classification as well
#' as a a column for each element of \code{features}. If \code{individual = TRUE} then there is an
#' additional column \code{idx} which gives the index of the \code{data} that each prediction corresponds to.}
#' \item{task.desc}{[\code{\link{TaskDesc}}]\cr
#' Task description.}
#' \item{target}{Target feature for regression, target feature levels for classification,
#' survival and event indicator for survival.}
#' \item{features}{[\code{character}]\cr
#' Features argument input.}
#' \item{interaction}{[\code{logical(1)}]\cr
#' Whether or not the features were interacted (i.e. conditioning).}
#' \item{derivative}{[\code{logical(1)}]\cr
#' Whether or not the partial derivative was estimated.}
#' \item{individual}{[\code{logical(1)}]\cr
#' Whether the partial dependences were aggregated or the individual curves are retained.}
#' \item{center}{[\code{logical(1)}]\cr
#' If \code{individual == TRUE} whether the partial dependence at the values of the
#' features specified was subtracted from the individual partial dependences. Only displayed if
#' \code{individual == TRUE}.}
#' @references
#' Goldstein, Alex, Adam Kapelner, Justin Bleich, and Emil Pitkin. \dQuote{Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation.} Journal of Computational and Graphical Statistics. Vol. 24, No. 1 (2015): 44-65.
#'
#' Friedman, Jerome. \dQuote{Greedy Function Approximation: A Gradient Boosting Machine.} The Annals of Statistics. Vol. 29. No. 5 (2001): 1189-1232.
#' @examples
#' lrn = makeLearner("regr.svm")
#' fit = train(lrn, bh.task)
#' pd = generatePartialDependenceData(fit, bh.task, "lstat")
#' plotPartialDependence(pd, data = getTaskData(bh.task))
#'
#' lrn = makeLearner("classif.rpart", predict.type = "prob")
#' fit = train(lrn, iris.task)
#' pd = generatePartialDependenceData(fit, iris.task, "Petal.Width")
#' plotPartialDependence(pd, data = getTaskData(iris.task))
#'
#' # simulated example with weights computed via the joint distribution
#' # in practice empirical weights could be constructed by estimating the joint
#' # density from the training data (the data arg to fun) and computing the probability
#' # of the prediction grid under this estimated density (the newdata arg) or
#' # by using something like data depth or outlier classification to weight the
#' # unusualness of points in arg newdata.
#' sigma = matrix(c(1, .5, .5, 1), 2, 2)
#' C = chol(sigma)
#' X = replicate(2, rnorm(100)) %*% C
#' alpha = runif(2, -1, 1)
#' y = X %*% alpha
#' df = data.frame(y, X)
#' tsk = makeRegrTask(data = df, target = "y")
#' fit = train("regr.svm", tsk)
#'
#' w.fun = function(x, newdata) {
#' # compute multivariate normal density given sigma
#' sigma = matrix(c(1, .5, .5, 1), 2, 2)
#' dec = chol(sigma)
#' tmp = backsolve(dec, t(newdata), transpose = TRUE)
#' rss = colSums(tmp^2)
#' logretval = -sum(log(diag(dec))) - 0.5 * ncol(newdata) * log(2 * pi) - 0.5 * rss
#' w = exp(logretval)
#' # weight prediction grid given probability of grid points under the joint
#' # density
#' sum(w * x) / sum(w)
#' }
#'
#' generatePartialDependenceData(fit, tsk, "X1", fun = w.fun)
#' @export
generatePartialDependenceData = function(obj, input, features,
interaction = FALSE, derivative = FALSE, individual = FALSE, center = NULL,
fun = mean, bounds = c(qnorm(.025), qnorm(.975)),
resample = "none", fmin, fmax, gridsize = 10L, range = NULL, ...) {
assertClass(obj, "WrappedModel")
if (obj$learner$predict.type == "se" & individual)
stop("individual = TRUE not compatabile with predict.type = 'se'!")
if (obj$learner$predict.type == "se" & derivative)
stop("derivative = TRUE is not compatible with predict.type = 'se'!")
if (!inherits(input, c("Task", "data.frame")))
stop("input must be a Task or a data.frame!")
if (inherits(input, "Task")) {
data = getTaskData(input)
td = input$task.desc
} else {
data = input
td = obj$task.desc
assertDataFrame(data, col.names = "unique", min.rows = 1L, min.cols = length(obj$features) + length(td$target))
assertSetEqual(colnames(data), c(obj$features, td$target), ordered = FALSE)
}
if (missing(features))
features = colnames(data)[!colnames(data) %in% td$target]
else
assertSubset(features, obj$features)
assertFlag(interaction)
assertFlag(derivative)
if (derivative & interaction)
stop("interaction cannot be TRUE if derivative is TRUE.")
if (derivative) {
if (any(sapply(data[, features, drop = FALSE], class) %in% c("factor", "ordered", "character")))
stop("All features must be numeric to estimate set derivative = TRUE!")
}
assertFlag(individual)
if (individual)
fun = function(x) x
if (!is.null(center)) {
if (derivative)
stop("center cannot be used with derivative = TRUE.")
assertList(center, len = length(features), names = "unique")
if (!all(names(center) %in% features))
stop("The names of the elements in center must be the same as the features.")
center = as.data.frame(do.call("cbind", center))
}
assertFunction(fun)
assertNumeric(bounds, len = 2L)
assertNumber(bounds[1], upper = 0)
assertNumber(bounds[2], lower = 0)
assertChoice(resample, c("none", "bootstrap", "subsample"))
if (missing(fmin))
fmin = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
min(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
if (missing(fmax))
fmax = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
max(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
assertList(fmin, len = length(features))
if (!all(names(fmin) %in% features))
stop("fmin must be a named list with an NA or value corresponding to each feature.")
assertList(fmax, len = length(features))
if (!all(names(fmax) %in% features))
stop("fmax must be a named list with an NA or value corresponding to each feature.")
assertCount(gridsize, positive = TRUE)
if (is.null(range))
rng = generateFeatureGrid(features, data, resample, gridsize, fmin, fmax)
else
rng = range
if (length(features) > 1L & interaction)
rng = expand.grid(rng)
if (td$type == "regr")
target = td$target
else if (td$type == "classif") {
if (length(td$class.levels) > 2L)
target = td$class.levels
else
target = td$positive
} else
target = "Risk"
args = list(obj = obj, data = data, fun = fun, td = td, individual = individual,
bounds = bounds, ...)
if (length(features) > 1L & !interaction) {
out = lapply(features, function(x) {
args$features = x
if (derivative) {
args$bounds = NULL
out = parallelMap(doPartialDerivativeIteration, x = rng[[x]], more.args = args)
rng = as.data.frame(rng[[x]])
colnames(rng) = x
centerpred = NULL
} else {
rng = as.data.frame(rng[[x]])
colnames(rng) = x
args$rng = rng
out = parallelMap(doPartialDependenceIteration, i = seq_len(nrow(rng)), more.args = args)
if (!is.null(center) & individual)
centerpred = as.data.frame(doPartialDependenceIteration(obj, data, center[, x, drop = FALSE],
x, fun, td, 1, bounds = bounds, ...))
else
centerpred = NULL
}
if (!individual)
doAggregatePartialDependence(out, td, target, x, rng)
else
doIndividualPartialDependence(out, td, nrow(data), rng, target, x, centerpred)
})
out = setDF(rbindlist(out, fill = TRUE))
} else {
args$features = features
if (derivative) {
args$bounds = NULL
out = parallelMap(doPartialDerivativeIteration, x = rng[[features]], more.args = args)
centerpred = NULL
rng = as.data.frame(rng)
colnames(rng) = features
} else {
rng = as.data.frame(rng)
colnames(rng) = features
args$rng = rng
out = parallelMap(doPartialDependenceIteration, i = seq_len(nrow(rng)), more.args = args)
if (!is.null(center) & individual)
centerpred = as.data.frame(doPartialDependenceIteration(obj, data, center, features, fun, td, 1, bounds))
else
centerpred = NULL
}
if (!individual)
out = doAggregatePartialDependence(out, td, target, features, rng)
else
out = doIndividualPartialDependence(out, td, nrow(data), rng, target, features, centerpred)
}
if (td$type %in% c("regr", "surv"))
out = out[, c(target, features, colnames(out)[!colnames(out) %in% c(target, features)])]
else
out = out[, c("Class", "Probability", features,
colnames(out)[!colnames(out) %in% c("Class", "Probability", features)])]
makeS3Obj("PartialDependenceData",
data = out,
task.desc = td,
target = target,
features = features,
interaction = interaction,
derivative = derivative,
individual = individual,
center = !is.null(center))
}
#' @title Generate a functional ANOVA decomposition
#'
#' @description
#' Decompose a learned prediction function as a sum of components estimated via partial dependence.
#'
#' @family partial_dependence functional_anova
#' @family generate_plot_data
#' @aliases FunctionalANOVAData
#'
#' @param obj [\code{\link{WrappedModel}}]\cr
#' Result of \code{\link{train}}.
#' @param input [\code{data.frame} | \code{\link{Task}}]\cr
#' Input data.
#' @param features [\code{character}]\cr
#' A vector of feature names contained in the training data.
#' If not specified all features in the \code{input} will be used.
#' @param depth [\code{integer(1)}]\cr
#' An integer indicating the depth of interaction amongst the features to compute. Default 1.
#' @param fun [\code{function}]\cr
#' A function that accepts a numeric vector and returns either a single number
#' such as a measure of location such as the mean, or three numbers, which give a lower bound,
#' a measure of location, and an upper bound. Note if three numbers are returned they must be
#' in this order. Two variables, \code{data} and \code{newdata} are made available to \code{fun} internally via a
#' wrapper. `data` is the training data from `input` and `newdata` contains a single point from the
#' prediction grid for \code{features} along with the training data for features not in \code{features}.
#' This allows the computation of weights based on comparisons of the prediction grid to the training data.
#' The default is the mean.
#' @param bounds [\code{numeric(2)}]\cr
#' The value (lower, upper) the estimated standard error is multiplied by to estimate the bound on a
#' confidence region for a partial dependence. Ignored if \code{predict.type != "se"} for the learner.
#' Default is the 2.5 and 97.5 quantiles (-1.96, 1.96) of the Gaussian distribution.
#' @param resample [\code{character(1)}]\cr
#' Defines how the prediction grid for each feature is created. If \dQuote{bootstrap} then
#' values are sampled with replacement from the training data. If \dQuote{subsample} then
#' values are sampled without replacement from the training data. If \dQuote{none} an evenly spaced
#' grid between either the empirical minimum and maximum, or the minimum and maximum defined by
#' \code{fmin} and \code{fmax}, is created.
#' Default is \dQuote{none}.
#' @param fmin [\code{numeric}]\cr
#' The minimum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = NULL} and when the empirical minimum is higher
#' than the theoretical minimum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical minimum of each numeric feature and NA for factor features.
#' @param fmax [\code{numeric}]\cr
#' The maximum value that each element of \code{features} can take.
#' This argument is only applicable if \code{resample = "none"} and when the empirical maximum is lower
#' than the theoretical maximum for a given feature. This only applies to numeric features and a
#' \code{NA} should be inserted into the vector if the corresponding feature is a factor.
#' Default is the empirical maximum of each numeric feature and NA for factor features.
#' @param gridsize [\code{integer(1)}]\cr
#' The length of the prediction grid created for each feature.
#' If \code{resample = "bootstrap"} or \code{resample = "subsample"} then this defines
#' the number of (possibly non-unique) values resampled. If \code{resample = NULL} it defines the
#' length of the evenly spaced grid created. Default 10.
#' @param ... additional arguments to be passed to \code{\link{predict}}.
#' @return [\code{FunctionalANOVAData}]. A named list, which contains the computed effects of the specified
#' depth amongst the features.
#'
#' Object members:
#' \item{data}{[\code{data.frame}]\cr
#' Has columns for the prediction: one column for regression and an additional two if bounds are used.
#' The \dQuote{effect} column specifies which features the prediction corresponds to.}
#' \item{task.desc}{[\code{\link{TaskDesc}}]\cr
#' Task description.}
#' \item{target}{The target feature for regression.}
#' \item{features}{[\code{character}]\cr
#' Features argument input.}
#' \item{interaction}{[\code{logical(1)}]\cr
#' Whether or not the \code{depth} is greater than 1.}
#' @references
#' Giles Hooker, \dQuote{Discovering additive structure in black box functions.} Proceedings of the 10th ACM SIGKDD international conference on Knowledge discovery and data mining (2004): 575-580.
#' @examples
#' fit = train("regr.rpart", bh.task)
#' fa = generateFunctionalANOVAData(fit, bh.task, c("lstat", "crim"), depth = 2L)
#' plotPartialDependence(fa)
#' @export
generateFunctionalANOVAData = function(obj, input, features, depth = 1L, fun = mean,
bounds = c(qnorm(.025), qnorm(.975)),
resample = "none", fmin, fmax, gridsize = 10L, ...) {
assertClass(obj, "WrappedModel")
if (!inherits(input, c("Task", "data.frame")))
stop("input must be a Task or a data.frame!")
if (inherits(input, "Task")) {
data = getTaskData(input)
td = input$task.desc
} else {
data = input
td = obj$task.desc
assertDataFrame(data, col.names = "unique", min.rows = 1L, min.cols = length(obj$features) + length(td$target))
assertSetEqual(colnames(data), c(obj$features, td$target), ordered = FALSE)
}
if (!td$type == "regr")
stop("only regression tasks are permitted")
excluded = colnames(data)
excluded = excluded[!excluded %in% c(features, td$target)]
assertChoice(resample, c("none", "bootstrap", "subsample"))
if (missing(fmin))
fmin = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
min(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
if (missing(fmax))
fmax = sapply(features, function(x) ifelse(is.ordered(data[[x]]) | is.numeric(data[[x]]),
max(data[[x]], na.rm = TRUE), NA), simplify = FALSE)
assertList(fmin, len = length(features))
if (!all(names(fmin) %in% features))
stop("fmin must be a named list with an NA or value corresponding to each feature.")
assertList(fmax, len = length(features))
if (!all(names(fmax) %in% features))
stop("fmax must be a named list with an NA or value corresponding to each feature.")
assertCount(gridsize, positive = TRUE)
assertIntegerish(depth, lower = 1L, upper = length(features), len = 1L)
assertFunction(fun)
assertNumeric(bounds, len = 2L)
assertNumber(bounds[1], upper = 0)
assertNumber(bounds[2], lower = 0)
## generate grid
fixed = generateFeatureGrid(features, data, resample, gridsize, fmin, fmax)
## generate list of effects to evaluate and associate with grid
U = unlist(lapply(1:depth, function(x) combn(features, x, simplify = FALSE)), recursive = FALSE)
depths = sapply(U, length)
effects = sapply(U, function(u) stri_paste(u, collapse = ":"))
fixed.grid = lapply(U, function(u) expand.grid(fixed[u]))
names(fixed.grid) = effects
target = td$target
## generate each effect
pd = lapply(U, function(u, args) {
args$features = u
args$rng = fixed.grid[[stri_paste(u, collapse = ":")]]
out = parallelMap(doPartialDependenceIteration, i = seq_len(nrow(args$rng)), more.args = args)
doAggregatePartialDependence(out, td, target, u, args$rng)
}, args = list(obj = obj, data = data, fun = fun, td = td, bounds = bounds, ...))
names(pd) = effects
if (all(c("upper", "lower") %in% colnames(pd[[1]])) |
obj$learner$predict.type == "se")
target = c("upper", "lower", target)
## remove lower order effects
f = lapply(U, function(u) {
hoe = pd[[stri_paste(u, collapse = ":")]]
if (length(u) > 1) {
sub = combn(u, length(u) - 1, simplify = FALSE)
loe = lapply(pd[unlist(sub)], function(x) {
to.match = colnames(x)[!(colnames(x) %in% target)]
out = merge(x, hoe[, to.match, drop = FALSE], by = to.match)
out[, colnames(out) %in% target]
})
hoe[, target] = hoe[, target] - Reduce("+", loe)
}
hoe
})
names(f) = effects
makeS3Obj(c("FunctionalANOVAData", "PartialDependenceData"),
data = setDF(rbindlist(f[depths == depth], fill = TRUE, idcol = "effect")),
task.desc = td,
target = target[!target %in% c("upper", "lower")],
features = features,
interaction = depth > 1L,
derivative = FALSE,
individual = FALSE,
center = FALSE)
}
#' @export
print.FunctionalANOVAData = function(x, ...) {
catf("FunctionalANOVAData")
catf("Task: %s", x$task.desc$id)
catf("Features: %s", stri_paste(x$features, collapse = ", "))
catf("Target: %s", stri_paste(x$target, collapse = ", "))
catf("Interaction Depth: %s", x$depth)
catf("Effects Computed: %s", stri_paste(levels(x$data$effect), collapse = ", "))
printHead(x$data, ...)
}
doPartialDerivativeIteration = function(x, obj, data, features, fun, td, individual, ...) {
fun.wrapper = function(x, newdata, data, ...) {
args = formals(fun)
if (all(c("newdata", "data") %in% names(args))) {
fun(x, newdata = newdata, data = data, ...)
} else if ("newdata" %in% names(args)) {
fun(x, newdata = newdata, ...)
} else if ("data" %in% names(args)) {
fun(x, data = data, ...)
} else {
fun(x, ...)
}
}
f = function(x, obj, data, features, fun, td, ...) {
newdata = data
newdata[features] = x
pred = do.call("predict", c(list("object" = obj, "newdata" = newdata), list(...)))
if (obj$learner$predict.type == "response")
fun(getPredictionResponse(pred), ...)
else if (length(obj$task.desc$class.levels) == 2L)
fun(getPredictionProbabilities(pred), ...)
else
apply(getPredictionProbabilities(pred), 2, fun, ...)
}
if (!individual) {
# construct function appropriate for numDeriv w/ aggregate predictions
if (obj$learner$predict.type == "response")
numDeriv::grad(func = f, x = x, obj = obj, data = data, features = features, fun = fun.wrapper, td = td, ...)
else
t(numDeriv::jacobian(func = f, x = x, obj = obj, data = data, features = features, fun = fun.wrapper, td = td, ...))
} else {
if (obj$learner$predict.type == "response")
sapply(seq_len(nrow(data)), function(idx)
numDeriv::grad(func = f, x = x, obj = obj, data = data[idx, , drop = FALSE],
features = features, fun = fun.wrapper, td = td, ...))
else
t(sapply(seq_len(nrow(data)), function(idx) numDeriv::jacobian(func = f, x = x, obj = obj,
data = data[idx, , drop = FALSE], features = features, fun = fun.wrapper, td = td, ...)))
}
}
doPartialDependenceIteration = function(obj, data, rng, features, fun, td, i, bounds, individual = FALSE, ...) {
newdata = data
newdata[features] = rng[i, ]
fun.wrapper = function(x, newdata, data, ...) {
args = formals(fun)
if (all(c("newdata", "data") %in% names(args))) {
fun(x, newdata = newdata, data = data, ...)
} else if ("newdata" %in% names(args)) {
fun(x, newdata = newdata, ...)
} else if ("data" %in% names(args)) {
fun(x, data = data, ...)
} else {
fun(x, ...)
}
}
pred = do.call("predict", c(list("object" = obj, "newdata" = newdata), list(...)))
if (obj$learner$predict.type == "response") {
fun.wrapper(getPredictionResponse(pred), newdata, data, ...)
} else if (length(obj$task.desc$class.levels) == 2L) {
fun.wrapper(getPredictionProbabilities(pred), newdata, data, ...)
} else if (obj$learner$predict.type == "se") {
point = getPredictionResponse(pred)
out = cbind(point + outer(getPredictionSE(pred), bounds), point)[, c(1, 3, 2)]
unname(apply(out, 2, fun.wrapper, newdata = newdata, data = data, ...))
} else {
apply(getPredictionProbabilities(pred), 2, fun.wrapper, newdata = newdata,
data = data, ...)
}
}
doAggregatePartialDependence = function(out, td, target, features, rng) {
out = as.data.frame(do.call("rbind", out))
if (td$type == "regr" & ncol(out) == 3L)
colnames(out) = c("lower", target, "upper")
else
colnames(out) = target
out = cbind(out, rng)
if (td$type == "regr" & all(c("upper", "lower", target) %in% colnames(out)))
if (!all(out$lower <= out[[target]] & out[[target]] <= out$upper))
stop("function argument must return a sorted numeric vector ordered lowest to highest.")
if (all(target %in% td$class.levels)) {
out = melt(out, id.vars = features, variable = "Class", value.name = "Probability", variable.factor = TRUE)
out$Class = stri_replace_all(out$Class, "", regex = "^prob\\.")
}
out
}
doIndividualPartialDependence = function(out, td, n, rng, target, features, centerpred = NULL) {
if (td$type == "classif" & length(td$class.levels) > 2L) {
if (!is.null(centerpred))
out = lapply(out, function(x) x - centerpred) else
out = lapply(out, as.data.frame)
out = as.data.frame(rbindlist(out))
colnames(out) = target
idx = rep(seq_len(n), nrow(rng))
rng = rng[rep(seq_len(nrow(rng)), each = n), , drop = FALSE]
out = cbind(out, rng, idx, row.names = NULL)
out = melt(out, id.vars = c(features, "idx"),
variable.name = "Class", value.name = "Probability", variable.factor = TRUE)
out$idx = interaction(out$idx, out$Class)
} else {
out = as.data.frame(setDT(transpose(out))) # see https://github.com/Rdatatable/data.table/issues/600
if (!is.null(centerpred))
out = out - setDF(transpose(rep(centerpred, nrow(out)))) #t(as.data.frame(lapply(out, function(x) unname(x - centerpred))))
colnames(out) = 1:n
out = cbind(out, rng)
out = melt(out, id.vars = features, variable.name = "idx", value.name = target)
if (td$type == "classif")
out = melt(out, id.vars = c(features, "idx"), value.name = "Probability",
variable.name = "Class", variable.factor = TRUE)
}
out
}
#' @export
print.PartialDependenceData = function(x, ...) {
catf("PartialDependenceData")
catf("Task: %s", x$task.desc$id)
catf("Features: %s", stri_paste(x$features, collapse = ", ", sep = " "))
catf("Target: %s", stri_paste(x$target, collapse = ", ", sep = " "))
catf("Derivative: %s", x$derivative)
catf("Interaction: %s", x$interaction)
catf("Individual: %s", x$individual)
if (x$individual)
catf("Predictions centered: %s", x$center)
printHead(x$data, ...)
}
#' @title Plot a partial dependence with ggplot2.
#' @description
#' Plot a partial dependence from \code{\link{generatePartialDependenceData}} using ggplot2.
#'
#' @family partial_dependence
#' @family plot
#'
#' @param obj [\code{PartialDependenceData}]\cr
#' Generated by \code{\link{generatePartialDependenceData}}.
#' @param geom [\code{charater(1)}]\cr
#' The type of geom to use to display the data. Can be \dQuote{line} or \dQuote{tile}.
#' For tiling at least two features must be used with \code{interaction = TRUE} in the call to
#' \code{\link{generatePartialDependenceData}}. This may be used in conjuction with the
#' \code{facet} argument if three features are specified in the call to
#' \code{\link{generatePartialDependenceData}}.
#' Default is \dQuote{line}.
#' @param facet [\code{character(1)}]\cr
#' The name of a feature to be used for facetting.
#' This feature must have been an element of the \code{features} argument to
#' \code{\link{generatePartialDependenceData}} and is only applicable when said argument had length
#' greater than 1.
#' The feature must be a factor or an integer.
#' If \code{\link{generatePartialDependenceData}} is called with the \code{interaction} argument \code{FALSE}
#' (the default) with argument \code{features} of length greater than one, then \code{facet} is ignored and
#' each feature is plotted in its own facet.
#' Default is \code{NULL}.
#' @template arg_facet_nrow_ncol
#' @param p [\code{numeric(1)}]\cr
#' If \code{individual = TRUE} then \code{sample} allows the user to sample without replacement
#' from the output to make the display more readable. Each row is sampled with probability \code{p}.
#' Default is \code{1}.
#' @param data [\code{data.frame}]\cr
#' Data points to plot. Usually the training data. For survival and binary classification tasks a rug plot
#' wherein ticks represent failures or instances of the positive class are shown. For regression tasks
#' points are shown. For multiclass classification tasks ticks are shown and colored according to their class.
#' Both the features and the target must be included.
#' Default is \code{NULL}.
#' @template ret_gg2
#' @export
plotPartialDependence = function(obj, geom = "line", facet = NULL, facet.wrap.nrow = NULL,
facet.wrap.ncol = NULL, p = 1, data = NULL) {
assertClass(obj, "PartialDependenceData")
assertChoice(geom, c("tile", "line"))
if (obj$interaction & length(obj$features) > 2L & geom != "tile")
stop("Cannot plot more than 2 features together with line plots.")
if (geom == "tile") {
if (!obj$interaction)
stop("obj argument created by generatePartialDependenceData was called with interaction = FALSE!")
}
if ("FunctionalANOVAData" %in% class(obj)) {
if (length(unique(obj$data$effect)) > 1L & obj$interaction)
stop("Cannot plot multiple ANOVA effects of depth > 1.")
}
if (!is.null(data)) {
assertDataFrame(data, col.names = "unique", min.rows = 1L,
min.cols = length(obj$features) + length(obj$td$target))
assertSubset(obj$features, colnames(data), empty.ok = FALSE)
}
if (!is.null(facet)) {
assertChoice(facet, obj$features)
if (!length(obj$features) %in% 2:3)
stop("obj argument created by generatePartialDependenceData must be called with two or three features to use this argument!")
if (!obj$interaction)
stop("obj argument created by generatePartialDependenceData must be called with interaction = TRUE to use this argument!")
features = obj$features[which(obj$features != facet)]
if (is.factor(obj$data[[facet]])) {
obj$data[[facet]] = stri_paste(facet, "=", obj$data[[facet]], sep = " ")
} else if (is.character(obj$data[[facet]])) {
obj$data[[facet]] = stri_paste(facet, "=", as.factor(obj$data[[facet]]), sep = " ")
} else if (is.numeric(obj$data[[facet]])) {
obj$data[[facet]] = stri_paste(facet, "=", as.factor(signif(obj$data[[facet]], 3L)), sep = " ")
} else {
stop("Invalid input to facet arg. Must refer to a numeric/integer, character, or facet feature.")
}
scales = "fixed"
} else {
features = obj$features
if (length(features) > 1L & !(length(features) == 2L & geom == "tile")) {
facet = "Feature"
scales = "free_x"
}
}
if (p != 1) {
assertNumber(p, lower = 0, upper = 1, finite = TRUE)
if (!obj$individual)
stop("obj argument created by generatePartialDependenceData must be called with individual = TRUE to use this argument!")
rows = unique(obj$data$idx)
id = sample(rows, size = floor(p * length(rows)))
obj$data = obj$data[which(obj$data$idx %in% id), ]
}
if (obj$task.desc$type %in% c("regr", "classif"))
target = obj$task.desc$target
else
target = "Risk"
bounds = all(c("lower", "upper") %in% colnames(obj$data) & obj$task.desc$type %in% c("surv", "regr") &
length(features) < 3L & geom == "line")
if (geom == "line") {
idx = which(sapply(obj$data, class) == "factor" & colnames(obj$data) %in% features)
# explicit casting previously done implicitly by reshape2::melt.data.frame
for (id in idx) obj$data[, id] = as.numeric(obj$data[, id])
obj$data = setDF(melt(data.table(obj$data),
id.vars = colnames(obj$data)[!colnames(obj$data) %in% features],
variable = "Feature", value.name = "Value", na.rm = TRUE, variable.factor = TRUE))
if (!obj$individual) {
if (obj$task.desc$type %in% c("regr", "surv"))
plt = ggplot(obj$data, aes_string("Value", target)) +
geom_line(color = ifelse(is.null(data), "black", "red")) + geom_point()
else
plt = ggplot(obj$data, aes_string("Value", "Probability", group = "Class", color = "Class")) +
geom_line() + geom_point()
} else {
if (obj$task.desc$type %in% c("regr", "surv")) {
plt = ggplot(obj$data, aes_string("Value", target, group = "idx")) +
geom_line(alpha = .25, color = ifelse(is.null(data), "black", "red")) + geom_point()
} else {
plt = ggplot(obj$data, aes_string("Value", "Probability", group = "idx", color = "Class")) +
geom_line(alpha = .25) + geom_point()
}
}
if (length(features) == 1L) {
if (obj$task.desc$type %in% c("regr", "surv"))
plt = plt + labs(x = features, y = target)
else
plt = plt + labs(x = features)
}
# bounds from fun or se estimation
if (bounds)
plt = plt + geom_ribbon(aes_string(ymin = "lower", ymax = "upper"), alpha = .5)
# labels for ice plots
if (obj$center)
plt = plt + ylab(stri_paste(target, "(centered)", sep = " "))
if (obj$derivative)
plt = plt + ylab(stri_paste(target, "(derivative)", sep = " "))
} else { ## tiling
if (obj$task.desc$type == "classif") {
target = "Probability"
facet = "Class"
scales = "free"
}
plt = ggplot(obj$data, aes_string(x = features[1], y = features[2], fill = target))
plt = plt + geom_raster(aes_string(fill = target))
# labels for ICE plots
if (obj$center)
plt = plt + scale_fill_continuous(guide = guide_colorbar(title = stri_paste(target, "(centered)", sep = " ")))
if (obj$derivative)
plt = plt + scale_fill_continuous(guide = guide_colorbar(title = stri_paste(target, "(derivative)", sep = " ")))
}
# facetting
if (!is.null(facet)) {
plt = plt + facet_wrap(as.formula(stri_paste("~", facet)), scales = scales,
nrow = facet.wrap.nrow, ncol = facet.wrap.ncol)
}
# data overplotting
if (!is.null(data)) {
data = data[, colnames(data) %in% c(obj$features, obj$task.desc$target)]
if (!is.null(facet)) {
if (!facet %in% obj$features)
data = melt(data, id.vars = c(obj$task.desc$target, obj$features[obj$features == facet]),
variable = "Feature", value.name = "Value", na.rm = TRUE, variable.factor = TRUE)
if (facet %in% obj$features) {
if (!is.factor(data[[facet]]))
data[[facet]] = stri_paste(facet, "=", as.factor(signif(data[[facet]], 2)), sep = " ")
else
data[[facet]] = stri_paste(facet, "=", data[[facet]], sep = " ")
}
}
if (geom == "line") {
if (obj$task.desc$type %in% c("classif", "surv")) {
if (obj$task.desc$type == "classif") {
if (!is.na(obj$task.desc$positive)) {
plt = plt + geom_rug(aes_string(plt$labels$x, color = obj$task.desc$target),
data[data[[obj$task.desc$target]] == obj$task.desc$positive, ],
alpha = .25, inherit.aes = FALSE)
} else {
plt = plt + geom_rug(aes_string(plt$labels$x), data, alpha = .25, inherit.aes = FALSE)
}
} else {
plt = plt + geom_rug(aes_string(plt$labels$x),
data[data[[obj$task.desc$target[2]]], ],
alpha = .25, inherit.aes = FALSE)
}
} else {
plt = plt + geom_point(aes_string(plt$labels$x, obj$task.desc$target),
data, alpha = .25, inherit.aes = FALSE)
}
} else {
plt = plt + geom_point(aes_string(plt$labels$x, plt$labels$y), data, alpha = .25, inherit.aes = FALSE)
}
}
plt
}
#' @title Plot a partial dependence using ggvis.
#' @description
#' Plot partial dependence from \code{\link{generatePartialDependenceData}} using ggvis.
#'
#' @family partial_dependence
#' @family plot
#'
#' @param obj [\code{PartialDependenceData}]\cr
#' Generated by \code{\link{generatePartialDependenceData}}.
#' @param interact [\code{character(1)}]\cr
#' The name of a feature to be mapped to an interactive sidebar using Shiny.
#' This feature must have been an element of the \code{features} argument to
#' \code{\link{generatePartialDependenceData}} and is only applicable when said argument had length
#' greater than 1.
#' If \code{\link{generatePartialDependenceData}} is called with the \code{interaction} argument \code{FALSE}
#' (the default) with argument \code{features} of length greater than one, then \code{interact} is ignored and
#' the feature displayed is controlled by an interactive side panel.
#' Default is \code{NULL}.
#' @param p [\code{numeric(1)}]\cr
#' If \code{individual = TRUE} then \code{sample} allows the user to sample without replacement
#' from the output to make the display more readable. Each row is sampled with probability \code{p}.
#' Default is \code{1}.
#' @template ret_ggv
#' @export
plotPartialDependenceGGVIS = function(obj, interact = NULL, p = 1) {
requirePackages("_ggvis")
assertClass(obj, "PartialDependenceData")
if (!is.null(interact))
assertChoice(interact, obj$features)
if (obj$interaction & length(obj$features) > 2L)
stop("It is only possible to plot 2 features with this function.")
if (!obj$interaction & !is.null(interact))
stop("obj argument created by generatePartialDependenceData was called with interaction = FALSE!")
if (p != 1) {
assertNumber(p, lower = 0, upper = 1, finite = TRUE)
if (!obj$individual)
stop("obj argument created by generatePartialDependenceData must be called with individual = TRUE to use this argument!")
rows = unique(obj$data$idx)
id = sample(rows, size = floor(p * length(rows)))
obj$data = obj$data[which(obj$data$idx %in% id), ]
}
if (obj$interaction & length(obj$features) == 2L) {
if (is.null(interact))
interact = obj$features[-which.max(sapply(obj$features, function(x) length(unique(obj$data[[x]]))))]
x = obj$features[which(obj$features != interact)]
if (is.factor(obj$data[[interact]]))
choices = levels(obj$data[[interact]])
else
choices = sort(unique(obj$data[[interact]]))
} else if (!obj$interaction & length(obj$features) > 1L) {
id = colnames(obj$data)[!colnames(obj$data) %in% obj$features]
obj$data = melt(obj$data, id.vars = id, variable.name = "Feature",
value.name = "Value", na.rm = TRUE, variable.factor = TRUE)
interact = "Feature"
choices = obj$features
} else
interact = NULL
bounds = all(c("lower", "upper") %in% colnames(obj$data) & obj$task.desc$type %in% c("surv", "regr"))
if (obj$task.desc$type %in% c("regr", "classif"))
target = obj$task.desc$target
else
target = "Risk"
createPlot = function(td, target, interaction, individual, data, x, bounds) {
classif = td$type == "classif" & all(target %in% td$class.levels)
if (classif) {
if (interaction)
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name("Probability")),
ggvis::prop("stroke", as.name("Class")))
else if (!interaction & !is.null(interact)) ## no interaction but multiple features
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name("Value")),
ggvis::prop("y", as.name("Probability")),
ggvis::prop("stroke", as.name("Class")))
else
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name("Probability")),
ggvis::prop("stroke", as.name("Class")))
} else { ## regression/survival
if (interaction)
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name(target)))
else if (!interaction & !is.null(interact))
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name("Value")),
ggvis::prop("y", as.name(target)))
else
plt = ggvis::ggvis(data,
ggvis::prop("x", as.name(x)),
ggvis::prop("y", as.name(target)))
}
if (bounds)
plt = ggvis::layer_ribbons(plt,
ggvis::prop("y", as.name("lower")),
ggvis::prop("y2", as.name("upper")),
ggvis::prop("opacity", .5))
if (individual) {
plt = ggvis::group_by_.ggvis(plt, as.name("idx"))
plt = ggvis::layer_paths(plt, ggvis::prop("opacity", .25))
} else {
if (classif)
plt = ggvis::layer_points(plt, ggvis::prop("fill", as.name("Class")))
else
plt = ggvis::layer_points(plt)
plt = ggvis::layer_lines(plt)
}
plt
}
if (obj$center)
header = stri_paste(target, "(centered)", sep = " ")
else if (obj$derivative)
header = stri_paste(target, "(derivative)", sep = " ")
else
header = target
if (!is.null(interact)) {
requirePackages("_shiny")
panel = shiny::selectInput("interaction_select", interact, choices)
ui = shiny::shinyUI(
shiny::pageWithSidebar(
shiny::headerPanel(header),
shiny::sidebarPanel(panel),
shiny::mainPanel(
shiny::uiOutput("ggvis_ui"),
ggvis::ggvisOutput("ggvis")
)
))
server = shiny::shinyServer(function(input, output) {
plt = shiny::reactive(createPlot(obj$task.desc, obj$target, obj$interaction, obj$individual,
obj$data[obj$data[[interact]] == input$interaction_select, ],
x, bounds))
ggvis::bind_shiny(plt, "ggvis", "ggvis_ui")
})
shiny::shinyApp(ui, server)
} else
createPlot(obj$task.desc, obj$target, obj$interaction, obj$individual, obj$data, obj$features, bounds)
}
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