The goal of this vignette is explain how to use
ResamplingSameOtherSizesCV for various kinds of
cross-validation.
Simulations
We begin with a simple simulated data set.
Comparing training on Same/Other/All subsets
N <- 2100
abs.x <- 70
set.seed(2)
x.vec <- runif(N, -abs.x, abs.x)
str(x.vec)
#> num [1:2100] -44.1 28.3 10.3 -46.5 62.1 ...
library(data.table)
(task.dt <- data.table(
x=x.vec,
y = sin(x.vec)+rnorm(N,sd=0.5)))
#> x y
#> <num> <num>
#> 1: -44.11648 -0.40781530
#> 2: 28.33237 -0.08520601
#> 3: 10.26569 -1.23266284
#> 4: -46.47273 -1.36225125
#> 5: 62.13751 -1.33779346
#> ---
#> 2096: 60.83765 -0.10678010
#> 2097: 55.71469 -0.92403513
#> 2098: 14.31045 1.04519820
#> 2099: 27.18008 1.67815828
#> 2100: 23.67202 -0.26881102
if(require(ggplot2)){
ggplot()+
geom_point(aes(
x, y),
shape=1,
data=task.dt)+
coord_equal()
}
#> Loading required package: ggplot2
Above we see a scatterplot of the simulated data. The goal of the learning algorithm will be to predict y from x.
The code below assigns three test groups to the randomly simulated data.
atomic.group.size <- 2
task.dt[, agroup := rep(seq(1, N/atomic.group.size), each=atomic.group.size)][]
#> x y agroup
#> <num> <num> <int>
#> 1: -44.11648 -0.40781530 1
#> 2: 28.33237 -0.08520601 1
#> 3: 10.26569 -1.23266284 2
#> 4: -46.47273 -1.36225125 2
#> 5: 62.13751 -1.33779346 3
#> ---
#> 2096: 60.83765 -0.10678010 1048
#> 2097: 55.71469 -0.92403513 1049
#> 2098: 14.31045 1.04519820 1049
#> 2099: 27.18008 1.67815828 1050
#> 2100: 23.67202 -0.26881102 1050
task.dt[, random_group := rep(
rep(c("A","B","B","C","C","C","C"), each=atomic.group.size),
l=.N
)][]
#> x y agroup random_group
#> <num> <num> <int> <char>
#> 1: -44.11648 -0.40781530 1 A
#> 2: 28.33237 -0.08520601 1 A
#> 3: 10.26569 -1.23266284 2 B
#> 4: -46.47273 -1.36225125 2 B
#> 5: 62.13751 -1.33779346 3 B
#> ---
#> 2096: 60.83765 -0.10678010 1048 C
#> 2097: 55.71469 -0.92403513 1049 C
#> 2098: 14.31045 1.04519820 1049 C
#> 2099: 27.18008 1.67815828 1050 C
#> 2100: 23.67202 -0.26881102 1050 C
table(group.tab <- task.dt$random_group)
#>
#> A B C
#> 300 600 1200The output above shows the number of rows in each random group. Below we define a task,
reg.task <- mlr3::TaskRegr$new(
"sin", task.dt, target="y")
reg.task$col_roles$group <- "agroup"
reg.task$col_roles$stratum <- "random_group"
reg.task$col_roles$feature <- "x"Note that if we assign the subset role at this point, we
will get an error, because this is not a standard mlr3 role.
reg.task$col_roles$subset <- "random_group"
#> Error in .__Task__col_roles(self = self, private = private, super = super, : Assertion on 'names of col_roles' failed: Names must be a permutation of set {'feature','target','name','order','stratum','group','weight'}, but has extra elements {'subset'}.Below we define the cross-validation object, which loads the
mlr3resampling package, and then we assign the random group column to be
used as the subset role.
same_other_sizes_cv <- mlr3resampling::ResamplingSameOtherSizesCV$new()
reg.task$col_roles$subset <- "random_group" Below we instantiate the resampler, in order to show details about
how it works (but normally you should not instantiate it yourself, as
this will be done automatically inside the call to
mlr3::benchmark).
same_other_sizes_cv$instantiate(reg.task)
same_other_sizes_cv$instance$iteration.dt
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: A all 700 1 43,44,57,58,71,72,...
#> 2: B all 700 1 3, 4, 5, 6,17,18,...
#> 3: C all 700 1 23,24,25,26,37,38,...
#> 4: A all 700 2 1, 2,15,16,29,30,...
#> 5: B all 700 2 33,34,47,48,61,62,...
#> 6: C all 700 2 13,14,21,22,35,36,...
#> 7: A all 700 3 99,100,155,156,169,170,...
#> 8: B all 700 3 19,20,45,46,75,76,...
#> 9: C all 700 3 7, 8, 9,10,11,12,...
#> 10: A other 600 1 43,44,57,58,71,72,...
#> 11: B other 500 1 3, 4, 5, 6,17,18,...
#> 12: C other 300 1 23,24,25,26,37,38,...
#> 13: A other 600 2 1, 2,15,16,29,30,...
#> 14: B other 500 2 33,34,47,48,61,62,...
#> 15: C other 300 2 13,14,21,22,35,36,...
#> 16: A other 600 3 99,100,155,156,169,170,...
#> 17: B other 500 3 19,20,45,46,75,76,...
#> 18: C other 300 3 7, 8, 9,10,11,12,...
#> 19: A same 100 1 43,44,57,58,71,72,...
#> 20: B same 200 1 3, 4, 5, 6,17,18,...
#> 21: C same 400 1 23,24,25,26,37,38,...
#> 22: A same 100 2 1, 2,15,16,29,30,...
#> 23: B same 200 2 33,34,47,48,61,62,...
#> 24: C same 400 2 13,14,21,22,35,36,...
#> 25: A same 100 3 99,100,155,156,169,170,...
#> 26: B same 200 3 19,20,45,46,75,76,...
#> 27: C same 400 3 7, 8, 9,10,11,12,...
#> test.subset train.subsets groups test.fold test
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 1, 2, 7, 8, 9,10,... 1 700 1
#> 2: 1, 2, 7, 8, 9,10,... 1 700 2
#> 3: 1, 2, 7, 8, 9,10,... 1 700 3
#> 4: 3,4,5,6,7,8,... 1 700 4
#> 5: 3,4,5,6,7,8,... 1 700 5
#> 6: 3,4,5,6,7,8,... 1 700 6
#> 7: 1,2,3,4,5,6,... 1 700 7
#> 8: 1,2,3,4,5,6,... 1 700 8
#> 9: 1,2,3,4,5,6,... 1 700 9
#> 10: 7, 8, 9,10,11,12,... 1 600 10
#> 11: 1, 2, 7, 8, 9,10,... 1 500 11
#> 12: 1, 2,15,16,19,20,... 1 300 12
#> 13: 3,4,5,6,7,8,... 1 600 13
#> 14: 7, 8, 9,10,11,12,... 1 500 14
#> 15: 3, 4, 5, 6,17,18,... 1 300 15
#> 16: 3, 4, 5, 6,13,14,... 1 600 16
#> 17: 1, 2,13,14,15,16,... 1 500 17
#> 18: 1,2,3,4,5,6,... 1 300 18
#> 19: 1, 2,15,16,29,30,... 1 100 19
#> 20: 19,20,33,34,45,46,... 1 200 20
#> 21: 7, 8, 9,10,11,12,... 1 400 21
#> 22: 43,44,57,58,71,72,... 1 100 22
#> 23: 3, 4, 5, 6,17,18,... 1 200 23
#> 24: 7, 8, 9,10,11,12,... 1 400 24
#> 25: 1, 2,15,16,29,30,... 1 100 25
#> 26: 3, 4, 5, 6,17,18,... 1 200 26
#> 27: 13,14,21,22,23,24,... 1 400 27
#> train seed n.train.groups iterationSo using the K-fold cross-validation, we will do one train/test split for each row of the table above. There is one row for each combination of test subset (A, B, C), train subset (same, other, all), and test fold (1, 2, 3).
We compute and plot the results using the code below,
(reg.learner.list <- list(
mlr3::LearnerRegrFeatureless$new()))
#> [[1]]
#> <LearnerRegrFeatureless:regr.featureless>: Featureless Regression Learner
#> * Model: -
#> * Parameters: robust=FALSE
#> * Packages: mlr3, stats
#> * Predict Types: [response], se, quantiles
#> * Feature Types: logical, integer, numeric, character, factor, ordered,
#> POSIXct
#> * Properties: featureless, importance, missings, selected_features
if(requireNamespace("rpart")){
reg.learner.list$rpart <- mlr3::LearnerRegrRpart$new()
}
#> Loading required namespace: rpart
(same.other.grid <- mlr3::benchmark_grid(
reg.task,
reg.learner.list,
same_other_sizes_cv))
#> task learner resampling
#> <char> <char> <char>
#> 1: sin regr.featureless same_other_sizes_cv
#> 2: sin regr.rpart same_other_sizes_cv
##if(require(future))plan("multisession")
lgr::get_logger("mlr3")$set_threshold("warn")
(same.other.result <- mlr3::benchmark(
same.other.grid, store_models = TRUE))
#> <BenchmarkResult> of 54 rows with 2 resampling runs
#> nr task_id learner_id resampling_id iters warnings errors
#> 1 sin regr.featureless same_other_sizes_cv 27 0 0
#> 2 sin regr.rpart same_other_sizes_cv 27 0 0
same.other.score <- mlr3resampling::score(same.other.result)
same.other.score[, n.train := sapply(train, length)]
same.other.score[1]
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: A all 700 1 43,44,57,58,71,72,...
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 1, 2, 7, 8, 9,10,... 1 700 1
#> uhash nr task task_id
#> <char> <int> <list> <char>
#> 1: dc9e29e1-79fb-4cb8-80ca-9a929d074a66 1 <TaskRegr:sin> sin
#> learner learner_id
#> <list> <char>
#> 1: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> resampling resampling_id prediction_test regr.mse
#> <list> <char> <list> <num>
#> 1: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.819815
#> algorithm n.train
#> <char> <int>
#> 1: featureless 1400
if(require(ggplot2)){
ggplot()+
geom_point(aes(
regr.mse, train.subsets, color=algorithm),
shape=1,
data=same.other.score)+
geom_text(aes(
Inf, train.subsets,
label=sprintf("n.train=%d ", n.train)),
hjust=1,
vjust=1.5,
data=same.other.score[algorithm=="featureless" & test.fold==1])+
facet_grid(. ~ test.subset, labeller=label_both, scales="free")+
scale_x_log10(
"Mean squared prediction error (test set)")
}
same.other.wide <- dcast(
same.other.score,
algorithm + test.subset + train.subsets ~ .,
list(mean, sd),
value.var="regr.mse")
if(require(ggplot2)){
ggplot()+
geom_segment(aes(
regr.mse_mean+regr.mse_sd, train.subsets,
xend=regr.mse_mean-regr.mse_sd, yend=train.subsets,
color=algorithm),
data=same.other.wide)+
geom_point(aes(
regr.mse_mean, train.subsets, color=algorithm),
shape=1,
data=same.other.wide)+
geom_text(aes(
Inf, train.subsets,
label=sprintf("n.train=%d ", n.train)),
hjust=1,
vjust=1.5,
data=same.other.score[algorithm=="featureless" & test.fold==1])+
facet_grid(. ~ test.subset, labeller=label_both, scales="free")+
scale_x_log10(
"Mean squared prediction error (test set)")
}
The figures above show a test subset in each panel, the train subsets on the y axis, the test error on the x axis, the two different algorithms are shown in two different colors. We can clearly see that
- For
train.subsets=same, test error is largest, sometimes almost as large as featureless, which is the error rate when no relationship has been learned between inputs and outputs (not enough data). - For
train.subsets=other, rpart test error is significantly smaller than featureless, indicating that some non-trivial relationship between inputs and outputs has been learned. Sometimes other has larger error than same, sometimes smaller (depending on sample size). - For
train.subsets=all, rpart test error tends to be minimal, which indicates that combining all of the subsets is beneficial in this case (when the pattern is exactly the same in the different subsets).
Overall in the plot above, all tends to have less prediction error than same, which suggests that the subsets are similar (and indeed there are iid in this simulation).
Below we visualize test error as a function of train size.
if(require(ggplot2)){
ggplot()+
geom_line(aes(
n.train, regr.mse,
color=algorithm,
group=paste(algorithm, test.fold)),
data=same.other.score)+
geom_label(aes(
n.train, regr.mse,
color=algorithm,
label=train.subsets),
data=same.other.score)+
facet_grid(. ~ test.subset, labeller=label_both, scales="free")+
scale_y_log10(
"Mean squared prediction error (test set)")
}
Downsample to see how many train data are required for good accuracy overall
In the previous section we defined a task using the
subset role, which means that the different values in that
column will be used to define different subsets for training/testing
using same/other/all CV. In contrast, below we define a task without the
subset role, which means that we will not have separate CV
iterations for same/other/all (full data is treated as one subset /
train subset is same).
task.no.subset <- mlr3::TaskRegr$new(
"sin", task.dt, target="y")
task.no.subset$col_roles$group <- "agroup"
task.no.subset$col_roles$stratum <- "random_group"
task.no.subset$col_roles$feature <- "x"
str(task.no.subset$col_roles)
#> List of 8
#> $ feature: chr "x"
#> $ target : chr "y"
#> $ name : chr(0)
#> $ order : chr(0)
#> $ stratum: chr "random_group"
#> $ group : chr "agroup"
#> $ weight : chr(0)
#> $ subset : chr(0)Below we define cross-validation, and we set the sizes
to 5 so we can see what happens when we have have train sets that are 5
sizes smaller than the full train set size.
same_other_sizes_cv <- mlr3resampling::ResamplingSameOtherSizesCV$new()
same_other_sizes_cv$param_set$values$sizes <- 5
same_other_sizes_cv$instantiate(task.no.subset)
same_other_sizes_cv$instance$iteration.dt
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: full same 700 1 3, 4,13,14,15,16,...
#> 2: full same 700 1 3, 4,13,14,15,16,...
#> 3: full same 700 1 3, 4,13,14,15,16,...
#> 4: full same 700 1 3, 4,13,14,15,16,...
#> 5: full same 700 1 3, 4,13,14,15,16,...
#> 6: full same 700 1 3, 4,13,14,15,16,...
#> 7: full same 700 2 1, 2,17,18,21,22,...
#> 8: full same 700 2 1, 2,17,18,21,22,...
#> 9: full same 700 2 1, 2,17,18,21,22,...
#> 10: full same 700 2 1, 2,17,18,21,22,...
#> 11: full same 700 2 1, 2,17,18,21,22,...
#> 12: full same 700 2 1, 2,17,18,21,22,...
#> 13: full same 700 3 5, 6, 7, 8, 9,10,...
#> 14: full same 700 3 5, 6, 7, 8, 9,10,...
#> 15: full same 700 3 5, 6, 7, 8, 9,10,...
#> 16: full same 700 3 5, 6, 7, 8, 9,10,...
#> 17: full same 700 3 5, 6, 7, 8, 9,10,...
#> 18: full same 700 3 5, 6, 7, 8, 9,10,...
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 565,566,583,584,743,744,... 1 21 1
#> 2: 133,134,171,172,305,306,... 1 43 2
#> 3: 77,78,93,94,95,96,... 1 87 3
#> 4: 7, 8,25,26,29,30,... 1 175 4
#> 5: 1, 2, 7, 8,17,18,... 1 350 5
#> 6: 1,2,5,6,7,8,... 1 700 6
#> 7: 39, 40,109,110,285,286,... 1 21 7
#> 8: 29,30,37,38,39,40,... 1 43 8
#> 9: 29,30,37,38,39,40,... 1 87 9
#> 10: 3, 4,13,14,23,24,... 1 175 10
#> 11: 3, 4,13,14,19,20,... 1 350 11
#> 12: 3,4,5,6,7,8,... 1 700 12
#> 13: 209,210,397,398,519,520,... 1 21 13
#> 14: 139,140,209,210,343,344,... 1 43 14
#> 15: 1, 2,17,18,43,44,... 1 87 15
#> 16: 1, 2,17,18,37,38,... 1 175 16
#> 17: 1, 2,13,14,17,18,... 1 350 17
#> 18: 1, 2, 3, 4,13,14,... 1 700 18So using the K-fold cross-validation, we will do one train/test split
for each row of the table above. There is one row for each combination
of n.train.groups (full train set size + 5 smaller sizes),
and test fold (1, 2, 3).
We compute and plot the results using the code below,
(reg.learner.list <- list(
mlr3::LearnerRegrFeatureless$new()))
#> [[1]]
#> <LearnerRegrFeatureless:regr.featureless>: Featureless Regression Learner
#> * Model: -
#> * Parameters: robust=FALSE
#> * Packages: mlr3, stats
#> * Predict Types: [response], se, quantiles
#> * Feature Types: logical, integer, numeric, character, factor, ordered,
#> POSIXct
#> * Properties: featureless, importance, missings, selected_features
if(requireNamespace("rpart")){
reg.learner.list$rpart <- mlr3::LearnerRegrRpart$new()
}
(same.other.grid <- mlr3::benchmark_grid(
task.no.subset,
reg.learner.list,
same_other_sizes_cv))
#> task learner resampling
#> <char> <char> <char>
#> 1: sin regr.featureless same_other_sizes_cv
#> 2: sin regr.rpart same_other_sizes_cv
##if(require(future))plan("multisession")
lgr::get_logger("mlr3")$set_threshold("warn")
(same.other.result <- mlr3::benchmark(
same.other.grid, store_models = TRUE))
#> <BenchmarkResult> of 36 rows with 2 resampling runs
#> nr task_id learner_id resampling_id iters warnings errors
#> 1 sin regr.featureless same_other_sizes_cv 18 0 0
#> 2 sin regr.rpart same_other_sizes_cv 18 0 0
same.other.score <- mlr3resampling::score(same.other.result)
same.other.score[, n.train := sapply(train, length)]
same.other.score[1]
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: full same 700 1 3, 4,13,14,15,16,...
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 565,566,583,584,743,744,... 1 21 1
#> uhash nr task task_id
#> <char> <int> <list> <char>
#> 1: 697995d1-ad26-41d9-aeda-f2e13990ea9b 1 <TaskRegr:sin> sin
#> learner learner_id
#> <list> <char>
#> 1: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> resampling resampling_id prediction_test regr.mse
#> <list> <char> <list> <num>
#> 1: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7650132
#> algorithm n.train
#> <char> <int>
#> 1: featureless 42
if(require(ggplot2)){
ggplot()+
geom_line(aes(
n.train, regr.mse,
color=algorithm,
group=paste(algorithm, test.fold)),
data=same.other.score)+
geom_point(aes(
n.train, regr.mse,
color=algorithm),
data=same.other.score)+
facet_grid(. ~ test.subset, labeller=label_both, scales="free")+
scale_x_log10(
"Number of train rows",
breaks=unique(same.other.score$n.train))+
scale_y_log10(
"Mean squared prediction error (test set)")
}
From the plot above, it looks like about 700 rows is enough to get minimal test error, using the rpart learner.
Downsample to sizes of other sets
N <- 600
abs.x <- 20
set.seed(1)
x.vec <- sort(runif(N, -abs.x, abs.x))
str(x.vec)
#> num [1:600] -19.9 -19.9 -19.7 -19.6 -19.6 ...
library(data.table)
(task.dt <- data.table(
x=x.vec,
y = sin(x.vec)+rnorm(N,sd=0.5)))
#> x y
#> <num> <num>
#> 1: -19.92653 -0.4336887
#> 2: -19.92269 -1.4023484
#> 3: -19.67486 0.2509134
#> 4: -19.55856 -0.8428921
#> 5: -19.55402 0.1794473
#> ---
#> 596: 19.70736 0.7497818
#> 597: 19.74997 0.3178435
#> 598: 19.75656 1.3950030
#> 599: 19.83862 -0.2086586
#> 600: 19.84309 0.5748863
if(require(ggplot2)){
ggplot()+
geom_point(aes(
x, y),
shape=1,
data=task.dt)+
coord_equal()
}
atomic.subset.size <- 2
task.dt[, agroup := rep(seq(1, N/atomic.subset.size), each=atomic.subset.size)][]
#> x y agroup
#> <num> <num> <int>
#> 1: -19.92653 -0.4336887 1
#> 2: -19.92269 -1.4023484 1
#> 3: -19.67486 0.2509134 2
#> 4: -19.55856 -0.8428921 2
#> 5: -19.55402 0.1794473 3
#> ---
#> 596: 19.70736 0.7497818 298
#> 597: 19.74997 0.3178435 299
#> 598: 19.75656 1.3950030 299
#> 599: 19.83862 -0.2086586 300
#> 600: 19.84309 0.5748863 300
task.dt[, random_subset := rep(
rep(c("A","B","B","B"), each=atomic.subset.size),
l=.N
)][]
#> x y agroup random_subset
#> <num> <num> <int> <char>
#> 1: -19.92653 -0.4336887 1 A
#> 2: -19.92269 -1.4023484 1 A
#> 3: -19.67486 0.2509134 2 B
#> 4: -19.55856 -0.8428921 2 B
#> 5: -19.55402 0.1794473 3 B
#> ---
#> 596: 19.70736 0.7497818 298 B
#> 597: 19.74997 0.3178435 299 B
#> 598: 19.75656 1.3950030 299 B
#> 599: 19.83862 -0.2086586 300 B
#> 600: 19.84309 0.5748863 300 B
table(subset.tab <- task.dt$random_subset)
#>
#> A B
#> 150 450
reg.task <- mlr3::TaskRegr$new(
"sin", task.dt, target="y")
reg.task$col_roles$subset <- "random_subset"
reg.task$col_roles$group <- "agroup"
reg.task$col_roles$stratum <- "random_subset"
reg.task$col_roles$feature <- "x"
same_other_sizes_cv <- mlr3resampling::ResamplingSameOtherSizesCV$new()In the previous section we analyzed prediction accuracy of
same/other/all, which corresponds to keeping sizes
parameter at default of -1. The main difference in this section is that
we change sizes to 0, which means to down-sample
same/other/all, so we can see if there is an effect for sample size
(there should be for iid problems with intermediate difficulty). We set
sizes to 0 in the next line:
same_other_sizes_cv$param_set$values$sizes <- 0
same_other_sizes_cv$instantiate(reg.task)
same_other_sizes_cv$instance$it
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: A all 200 1 1, 2,49,50,57,58,...
#> 2: A all 200 1 1, 2,49,50,57,58,...
#> 3: A all 200 1 1, 2,49,50,57,58,...
#> 4: B all 200 1 19,20,31,32,37,38,...
#> 5: B all 200 1 19,20,31,32,37,38,...
#> 6: B all 200 1 19,20,31,32,37,38,...
#> 7: A all 200 2 17,18,41,42,89,90,...
#> 8: A all 200 2 17,18,41,42,89,90,...
#> 9: A all 200 2 17,18,41,42,89,90,...
#> 10: B all 200 2 3,4,5,6,7,8,...
#> 11: B all 200 2 3,4,5,6,7,8,...
#> 12: B all 200 2 3,4,5,6,7,8,...
#> 13: A all 200 3 9,10,25,26,33,34,...
#> 14: A all 200 3 9,10,25,26,33,34,...
#> 15: A all 200 3 9,10,25,26,33,34,...
#> 16: B all 200 3 15,16,21,22,23,24,...
#> 17: B all 200 3 15,16,21,22,23,24,...
#> 18: B all 200 3 15,16,21,22,23,24,...
#> 19: A other 150 1 1, 2,49,50,57,58,...
#> 20: A other 150 1 1, 2,49,50,57,58,...
#> 21: B other 50 1 19,20,31,32,37,38,...
#> 22: A other 150 2 17,18,41,42,89,90,...
#> 23: A other 150 2 17,18,41,42,89,90,...
#> 24: B other 50 2 3,4,5,6,7,8,...
#> 25: A other 150 3 9,10,25,26,33,34,...
#> 26: A other 150 3 9,10,25,26,33,34,...
#> 27: B other 50 3 15,16,21,22,23,24,...
#> 28: A same 50 1 1, 2,49,50,57,58,...
#> 29: B same 150 1 19,20,31,32,37,38,...
#> 30: B same 150 1 19,20,31,32,37,38,...
#> 31: A same 50 2 17,18,41,42,89,90,...
#> 32: B same 150 2 3,4,5,6,7,8,...
#> 33: B same 150 2 3,4,5,6,7,8,...
#> 34: A same 50 3 9,10,25,26,33,34,...
#> 35: B same 150 3 15,16,21,22,23,24,...
#> 36: B same 150 3 15,16,21,22,23,24,...
#> test.subset train.subsets groups test.fold test
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 5, 6, 9,10,15,16,... 1 50 1
#> 2: 3,4,5,6,7,8,... 1 150 2
#> 3: 3,4,5,6,7,8,... 1 200 3
#> 4: 3, 4, 7, 8,15,16,... 1 50 4
#> 5: 3,4,5,6,7,8,... 1 150 5
#> 6: 3,4,5,6,7,8,... 1 200 6
#> 7: 1, 2,35,36,39,40,... 1 50 7
#> 8: 1, 2, 9,10,19,20,... 1 150 8
#> 9: 1, 2, 9,10,15,16,... 1 200 9
#> 10: 19,20,63,64,73,74,... 1 50 10
#> 11: 1, 2, 9,10,15,16,... 1 150 11
#> 12: 1, 2, 9,10,15,16,... 1 200 12
#> 13: 29,30,37,38,49,50,... 1 50 13
#> 14: 5, 6,11,12,13,14,... 1 150 14
#> 15: 1,2,3,4,5,6,... 1 200 15
#> 16: 13,14,29,30,49,50,... 1 50 16
#> 17: 1,2,3,4,5,6,... 1 150 17
#> 18: 1,2,3,4,5,6,... 1 200 18
#> 19: 15,16,21,22,55,56,... 1 50 19
#> 20: 3,4,5,6,7,8,... 1 150 20
#> 21: 9,10,17,18,25,26,... 1 50 21
#> 22: 15,16,19,20,23,24,... 1 50 22
#> 23: 15,16,19,20,21,22,... 1 150 23
#> 24: 1, 2, 9,10,25,26,... 1 50 24
#> 25: 11,12,19,20,27,28,... 1 50 25
#> 26: 3,4,5,6,7,8,... 1 150 26
#> 27: 1, 2,17,18,41,42,... 1 50 27
#> 28: 9,10,17,18,25,26,... 1 50 28
#> 29: 59,60,63,64,75,76,... 1 50 29
#> 30: 3,4,5,6,7,8,... 1 150 30
#> 31: 1, 2, 9,10,25,26,... 1 50 31
#> 32: 23,24,37,38,51,52,... 1 50 32
#> 33: 15,16,19,20,21,22,... 1 150 33
#> 34: 1, 2,17,18,41,42,... 1 50 34
#> 35: 11,12,19,20,45,46,... 1 50 35
#> 36: 3,4,5,6,7,8,... 1 150 36
#> train seed n.train.groups iteration
(reg.learner.list <- list(
mlr3::LearnerRegrFeatureless$new()))
#> [[1]]
#> <LearnerRegrFeatureless:regr.featureless>: Featureless Regression Learner
#> * Model: -
#> * Parameters: robust=FALSE
#> * Packages: mlr3, stats
#> * Predict Types: [response], se, quantiles
#> * Feature Types: logical, integer, numeric, character, factor, ordered,
#> POSIXct
#> * Properties: featureless, importance, missings, selected_features
if(requireNamespace("rpart")){
reg.learner.list$rpart <- mlr3::LearnerRegrRpart$new()
}
(same.other.grid <- mlr3::benchmark_grid(
reg.task,
reg.learner.list,
same_other_sizes_cv))
#> task learner resampling
#> <char> <char> <char>
#> 1: sin regr.featureless same_other_sizes_cv
#> 2: sin regr.rpart same_other_sizes_cv
##if(require(future))plan("multisession")
lgr::get_logger("mlr3")$set_threshold("warn")
(same.other.result <- mlr3::benchmark(
same.other.grid, store_models = TRUE))
#> <BenchmarkResult> of 72 rows with 2 resampling runs
#> nr task_id learner_id resampling_id iters warnings errors
#> 1 sin regr.featureless same_other_sizes_cv 36 0 0
#> 2 sin regr.rpart same_other_sizes_cv 36 0 0
same.other.score <- mlr3resampling::score(same.other.result)
same.other.score[1]
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: A all 200 1 1, 2,49,50,57,58,...
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 5, 6, 9,10,15,16,... 1 50 1
#> uhash nr task task_id
#> <char> <int> <list> <char>
#> 1: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> learner learner_id
#> <list> <char>
#> 1: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> resampling resampling_id prediction_test regr.mse
#> <list> <char> <list> <num>
#> 1: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5814085
#> algorithm
#> <char>
#> 1: featurelessThe plot below shows the same results (no down-sampling) as if we did
sizes=-1 (like in the previous section.
if(require(ggplot2)){
ggplot()+
geom_point(aes(
regr.mse, train.subsets, color=algorithm),
shape=1,
data=same.other.score[groups==n.train.groups])+
facet_grid(. ~ test.subset, labeller=label_both)
}
The plots below compare all six train subsets (including three down-sampled), and it it is clear there is an effect for sample size.
same.other.score[, subset.N := paste(train.subsets, n.train.groups)][]
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: A all 200 1 1, 2,49,50,57,58,...
#> 2: A all 200 1 1, 2,49,50,57,58,...
#> 3: A all 200 1 1, 2,49,50,57,58,...
#> 4: B all 200 1 19,20,31,32,37,38,...
#> 5: B all 200 1 19,20,31,32,37,38,...
#> 6: B all 200 1 19,20,31,32,37,38,...
#> 7: A all 200 2 17,18,41,42,89,90,...
#> 8: A all 200 2 17,18,41,42,89,90,...
#> 9: A all 200 2 17,18,41,42,89,90,...
#> 10: B all 200 2 3,4,5,6,7,8,...
#> 11: B all 200 2 3,4,5,6,7,8,...
#> 12: B all 200 2 3,4,5,6,7,8,...
#> 13: A all 200 3 9,10,25,26,33,34,...
#> 14: A all 200 3 9,10,25,26,33,34,...
#> 15: A all 200 3 9,10,25,26,33,34,...
#> 16: B all 200 3 15,16,21,22,23,24,...
#> 17: B all 200 3 15,16,21,22,23,24,...
#> 18: B all 200 3 15,16,21,22,23,24,...
#> 19: A other 150 1 1, 2,49,50,57,58,...
#> 20: A other 150 1 1, 2,49,50,57,58,...
#> 21: B other 50 1 19,20,31,32,37,38,...
#> 22: A other 150 2 17,18,41,42,89,90,...
#> 23: A other 150 2 17,18,41,42,89,90,...
#> 24: B other 50 2 3,4,5,6,7,8,...
#> 25: A other 150 3 9,10,25,26,33,34,...
#> 26: A other 150 3 9,10,25,26,33,34,...
#> 27: B other 50 3 15,16,21,22,23,24,...
#> 28: A same 50 1 1, 2,49,50,57,58,...
#> 29: B same 150 1 19,20,31,32,37,38,...
#> 30: B same 150 1 19,20,31,32,37,38,...
#> 31: A same 50 2 17,18,41,42,89,90,...
#> 32: B same 150 2 3,4,5,6,7,8,...
#> 33: B same 150 2 3,4,5,6,7,8,...
#> 34: A same 50 3 9,10,25,26,33,34,...
#> 35: B same 150 3 15,16,21,22,23,24,...
#> 36: B same 150 3 15,16,21,22,23,24,...
#> 37: A all 200 1 1, 2,49,50,57,58,...
#> 38: A all 200 1 1, 2,49,50,57,58,...
#> 39: A all 200 1 1, 2,49,50,57,58,...
#> 40: B all 200 1 19,20,31,32,37,38,...
#> 41: B all 200 1 19,20,31,32,37,38,...
#> 42: B all 200 1 19,20,31,32,37,38,...
#> 43: A all 200 2 17,18,41,42,89,90,...
#> 44: A all 200 2 17,18,41,42,89,90,...
#> 45: A all 200 2 17,18,41,42,89,90,...
#> 46: B all 200 2 3,4,5,6,7,8,...
#> 47: B all 200 2 3,4,5,6,7,8,...
#> 48: B all 200 2 3,4,5,6,7,8,...
#> 49: A all 200 3 9,10,25,26,33,34,...
#> 50: A all 200 3 9,10,25,26,33,34,...
#> 51: A all 200 3 9,10,25,26,33,34,...
#> 52: B all 200 3 15,16,21,22,23,24,...
#> 53: B all 200 3 15,16,21,22,23,24,...
#> 54: B all 200 3 15,16,21,22,23,24,...
#> 55: A other 150 1 1, 2,49,50,57,58,...
#> 56: A other 150 1 1, 2,49,50,57,58,...
#> 57: B other 50 1 19,20,31,32,37,38,...
#> 58: A other 150 2 17,18,41,42,89,90,...
#> 59: A other 150 2 17,18,41,42,89,90,...
#> 60: B other 50 2 3,4,5,6,7,8,...
#> 61: A other 150 3 9,10,25,26,33,34,...
#> 62: A other 150 3 9,10,25,26,33,34,...
#> 63: B other 50 3 15,16,21,22,23,24,...
#> 64: A same 50 1 1, 2,49,50,57,58,...
#> 65: B same 150 1 19,20,31,32,37,38,...
#> 66: B same 150 1 19,20,31,32,37,38,...
#> 67: A same 50 2 17,18,41,42,89,90,...
#> 68: B same 150 2 3,4,5,6,7,8,...
#> 69: B same 150 2 3,4,5,6,7,8,...
#> 70: A same 50 3 9,10,25,26,33,34,...
#> 71: B same 150 3 15,16,21,22,23,24,...
#> 72: B same 150 3 15,16,21,22,23,24,...
#> test.subset train.subsets groups test.fold test
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 5, 6, 9,10,15,16,... 1 50 1
#> 2: 3,4,5,6,7,8,... 1 150 2
#> 3: 3,4,5,6,7,8,... 1 200 3
#> 4: 3, 4, 7, 8,15,16,... 1 50 4
#> 5: 3,4,5,6,7,8,... 1 150 5
#> 6: 3,4,5,6,7,8,... 1 200 6
#> 7: 1, 2,35,36,39,40,... 1 50 7
#> 8: 1, 2, 9,10,19,20,... 1 150 8
#> 9: 1, 2, 9,10,15,16,... 1 200 9
#> 10: 19,20,63,64,73,74,... 1 50 10
#> 11: 1, 2, 9,10,15,16,... 1 150 11
#> 12: 1, 2, 9,10,15,16,... 1 200 12
#> 13: 29,30,37,38,49,50,... 1 50 13
#> 14: 5, 6,11,12,13,14,... 1 150 14
#> 15: 1,2,3,4,5,6,... 1 200 15
#> 16: 13,14,29,30,49,50,... 1 50 16
#> 17: 1,2,3,4,5,6,... 1 150 17
#> 18: 1,2,3,4,5,6,... 1 200 18
#> 19: 15,16,21,22,55,56,... 1 50 19
#> 20: 3,4,5,6,7,8,... 1 150 20
#> 21: 9,10,17,18,25,26,... 1 50 21
#> 22: 15,16,19,20,23,24,... 1 50 22
#> 23: 15,16,19,20,21,22,... 1 150 23
#> 24: 1, 2, 9,10,25,26,... 1 50 24
#> 25: 11,12,19,20,27,28,... 1 50 25
#> 26: 3,4,5,6,7,8,... 1 150 26
#> 27: 1, 2,17,18,41,42,... 1 50 27
#> 28: 9,10,17,18,25,26,... 1 50 28
#> 29: 59,60,63,64,75,76,... 1 50 29
#> 30: 3,4,5,6,7,8,... 1 150 30
#> 31: 1, 2, 9,10,25,26,... 1 50 31
#> 32: 23,24,37,38,51,52,... 1 50 32
#> 33: 15,16,19,20,21,22,... 1 150 33
#> 34: 1, 2,17,18,41,42,... 1 50 34
#> 35: 11,12,19,20,45,46,... 1 50 35
#> 36: 3,4,5,6,7,8,... 1 150 36
#> 37: 5, 6, 9,10,15,16,... 1 50 1
#> 38: 3,4,5,6,7,8,... 1 150 2
#> 39: 3,4,5,6,7,8,... 1 200 3
#> 40: 3, 4, 7, 8,15,16,... 1 50 4
#> 41: 3,4,5,6,7,8,... 1 150 5
#> 42: 3,4,5,6,7,8,... 1 200 6
#> 43: 1, 2,35,36,39,40,... 1 50 7
#> 44: 1, 2, 9,10,19,20,... 1 150 8
#> 45: 1, 2, 9,10,15,16,... 1 200 9
#> 46: 19,20,63,64,73,74,... 1 50 10
#> 47: 1, 2, 9,10,15,16,... 1 150 11
#> 48: 1, 2, 9,10,15,16,... 1 200 12
#> 49: 29,30,37,38,49,50,... 1 50 13
#> 50: 5, 6,11,12,13,14,... 1 150 14
#> 51: 1,2,3,4,5,6,... 1 200 15
#> 52: 13,14,29,30,49,50,... 1 50 16
#> 53: 1,2,3,4,5,6,... 1 150 17
#> 54: 1,2,3,4,5,6,... 1 200 18
#> 55: 15,16,21,22,55,56,... 1 50 19
#> 56: 3,4,5,6,7,8,... 1 150 20
#> 57: 9,10,17,18,25,26,... 1 50 21
#> 58: 15,16,19,20,23,24,... 1 50 22
#> 59: 15,16,19,20,21,22,... 1 150 23
#> 60: 1, 2, 9,10,25,26,... 1 50 24
#> 61: 11,12,19,20,27,28,... 1 50 25
#> 62: 3,4,5,6,7,8,... 1 150 26
#> 63: 1, 2,17,18,41,42,... 1 50 27
#> 64: 9,10,17,18,25,26,... 1 50 28
#> 65: 59,60,63,64,75,76,... 1 50 29
#> 66: 3,4,5,6,7,8,... 1 150 30
#> 67: 1, 2, 9,10,25,26,... 1 50 31
#> 68: 23,24,37,38,51,52,... 1 50 32
#> 69: 15,16,19,20,21,22,... 1 150 33
#> 70: 1, 2,17,18,41,42,... 1 50 34
#> 71: 11,12,19,20,45,46,... 1 50 35
#> 72: 3,4,5,6,7,8,... 1 150 36
#> train seed n.train.groups iteration
#> uhash nr task task_id
#> <char> <int> <list> <char>
#> 1: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 2: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 3: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 4: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 5: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 6: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 7: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 8: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 9: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 10: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 11: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 12: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 13: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 14: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 15: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 16: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 17: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 18: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 19: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 20: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 21: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 22: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 23: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 24: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 25: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 26: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 27: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 28: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 29: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 30: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 31: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 32: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 33: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 34: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 35: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 36: ff27df21-eb43-4113-be49-5c5f1479d6a8 1 <TaskRegr:sin> sin
#> 37: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 38: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 39: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 40: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 41: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 42: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 43: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 44: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 45: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 46: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 47: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 48: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 49: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 50: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 51: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 52: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 53: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 54: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 55: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 56: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 57: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 58: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 59: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 60: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 61: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 62: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 63: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 64: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 65: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 66: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 67: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 68: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 69: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 70: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 71: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> 72: c20651ab-ff3a-4e62-9a23-241c25bf0f75 2 <TaskRegr:sin> sin
#> uhash nr task task_id
#> learner learner_id
#> <list> <char>
#> 1: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 2: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 3: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 4: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 5: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 6: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 7: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 8: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 9: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 10: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 11: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 12: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 13: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 14: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 15: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 16: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 17: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 18: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 19: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 20: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 21: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 22: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 23: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 24: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 25: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 26: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 27: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 28: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 29: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 30: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 31: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 32: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 33: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 34: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 35: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 36: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> 37: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 38: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 39: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 40: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 41: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 42: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 43: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 44: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 45: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 46: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 47: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 48: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 49: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 50: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 51: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 52: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 53: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 54: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 55: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 56: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 57: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 58: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 59: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 60: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 61: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 62: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 63: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 64: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 65: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 66: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 67: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 68: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 69: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 70: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 71: <LearnerRegrRpart:regr.rpart> regr.rpart
#> 72: <LearnerRegrRpart:regr.rpart> regr.rpart
#> learner learner_id
#> resampling resampling_id prediction_test regr.mse
#> <list> <char> <list> <num>
#> 1: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5814085
#> 2: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5888123
#> 3: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6004137
#> 4: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7418338
#> 5: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7448785
#> 6: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7426736
#> 7: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7032864
#> 8: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6915582
#> 9: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6935124
#> 10: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6876009
#> 11: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6938962
#> 12: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6927970
#> 13: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8679940
#> 14: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8679637
#> 15: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8698560
#> 16: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8100344
#> 17: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8080412
#> 18: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8079158
#> 19: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6008614
#> 20: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5986958
#> 21: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7438359
#> 22: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7575599
#> 23: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6927668
#> 24: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6974565
#> 25: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8758799
#> 26: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8682078
#> 27: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8095930
#> 28: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6058833
#> 29: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7644929
#> 30: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7423914
#> 31: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6967243
#> 32: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7065626
#> 33: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6915689
#> 34: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8800099
#> 35: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8944441
#> 36: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8090933
#> 37: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.9579886
#> 38: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5572793
#> 39: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5762640
#> 40: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6754320
#> 41: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4605665
#> 42: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4170070
#> 43: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7317229
#> 44: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5239765
#> 45: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.3890640
#> 46: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7954012
#> 47: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.3448899
#> 48: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.3294351
#> 49: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5894307
#> 50: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5876353
#> 51: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5989192
#> 52: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6718522
#> 53: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4275034
#> 54: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5398954
#> 55: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7813902
#> 56: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6348613
#> 57: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5887354
#> 58: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6004308
#> 59: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4871282
#> 60: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5600961
#> 61: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7225103
#> 62: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4658216
#> 63: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7620797
#> 64: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.8782663
#> 65: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7809353
#> 66: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4280411
#> 67: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6343650
#> 68: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.6115182
#> 69: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4005002
#> 70: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.7486917
#> 71: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.9276521
#> 72: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.4816441
#> resampling resampling_id prediction_test regr.mse
#> algorithm subset.N
#> <char> <char>
#> 1: featureless all 50
#> 2: featureless all 150
#> 3: featureless all 200
#> 4: featureless all 50
#> 5: featureless all 150
#> 6: featureless all 200
#> 7: featureless all 50
#> 8: featureless all 150
#> 9: featureless all 200
#> 10: featureless all 50
#> 11: featureless all 150
#> 12: featureless all 200
#> 13: featureless all 50
#> 14: featureless all 150
#> 15: featureless all 200
#> 16: featureless all 50
#> 17: featureless all 150
#> 18: featureless all 200
#> 19: featureless other 50
#> 20: featureless other 150
#> 21: featureless other 50
#> 22: featureless other 50
#> 23: featureless other 150
#> 24: featureless other 50
#> 25: featureless other 50
#> 26: featureless other 150
#> 27: featureless other 50
#> 28: featureless same 50
#> 29: featureless same 50
#> 30: featureless same 150
#> 31: featureless same 50
#> 32: featureless same 50
#> 33: featureless same 150
#> 34: featureless same 50
#> 35: featureless same 50
#> 36: featureless same 150
#> 37: rpart all 50
#> 38: rpart all 150
#> 39: rpart all 200
#> 40: rpart all 50
#> 41: rpart all 150
#> 42: rpart all 200
#> 43: rpart all 50
#> 44: rpart all 150
#> 45: rpart all 200
#> 46: rpart all 50
#> 47: rpart all 150
#> 48: rpart all 200
#> 49: rpart all 50
#> 50: rpart all 150
#> 51: rpart all 200
#> 52: rpart all 50
#> 53: rpart all 150
#> 54: rpart all 200
#> 55: rpart other 50
#> 56: rpart other 150
#> 57: rpart other 50
#> 58: rpart other 50
#> 59: rpart other 150
#> 60: rpart other 50
#> 61: rpart other 50
#> 62: rpart other 150
#> 63: rpart other 50
#> 64: rpart same 50
#> 65: rpart same 50
#> 66: rpart same 150
#> 67: rpart same 50
#> 68: rpart same 50
#> 69: rpart same 150
#> 70: rpart same 50
#> 71: rpart same 50
#> 72: rpart same 150
#> algorithm subset.N
(levs <- same.other.score[order(train.subsets, n.train.groups), unique(subset.N)])
#> [1] "all 50" "all 150" "all 200" "other 50" "other 150" "same 50"
#> [7] "same 150"
same.other.score[, subset.N.fac := factor(subset.N, levs)]
if(require(ggplot2)){
ggplot()+
geom_point(aes(
regr.mse, subset.N.fac, color=algorithm),
shape=1,
data=same.other.score)+
facet_wrap("test.subset", labeller=label_both, scales="free", nrow=1)
}
(levs <- same.other.score[order(n.train.groups, train.subsets), unique(subset.N)])
#> [1] "all 50" "other 50" "same 50" "all 150" "other 150" "same 150"
#> [7] "all 200"
same.other.score[, N.subset.fac := factor(subset.N, levs)]
if(require(ggplot2)){
ggplot()+
geom_point(aes(
regr.mse, N.subset.fac, color=algorithm),
shape=1,
data=same.other.score)+
facet_wrap("test.subset", labeller=label_both, scales="free", nrow=1)
}
Another way to view the effect of sample size is to plot the test/prediction error, as a function of number of train data, as in the plots below.
if(require(ggplot2)){
ggplot()+
geom_point(aes(
n.train.groups, regr.mse,
color=train.subsets),
shape=1,
data=same.other.score)+
geom_line(aes(
n.train.groups, regr.mse,
group=paste(train.subsets, seed, algorithm),
linetype=algorithm,
color=train.subsets),
data=same.other.score)+
facet_grid(test.fold ~ test.subset, labeller=label_both)+
scale_x_log10()
}
rpart.score <- same.other.score[algorithm=="rpart" & train.subsets != "other"]
if(require(ggplot2)){
ggplot()+
geom_point(aes(
n.train.groups, regr.mse,
color=train.subsets),
shape=1,
data=rpart.score)+
geom_line(aes(
n.train.groups, regr.mse,
group=paste(train.subsets, seed, algorithm),
color=train.subsets),
data=rpart.score)+
facet_grid(test.fold ~ test.subset, labeller=label_both)+
scale_x_log10()
}
Use with auto_tuner on a task with stratification and grouping
In this section we show how ResamplingSameOtherSizesCV
can be used on a task with stratification and grouping, for
hyper-parameter learning. First we recall the previously defined task
and evaluation CV.
str(reg.task$col_roles)
#> List of 8
#> $ feature: chr "x"
#> $ target : chr "y"
#> $ name : chr(0)
#> $ order : chr(0)
#> $ stratum: chr "random_subset"
#> $ group : chr "agroup"
#> $ weight : chr(0)
#> $ subset : chr "random_subset"We see in the output aove that the task has column roles for both
stratum and group, which normally errors when
used with ResamplingCV:
mlr3::ResamplingCV$new()$instantiate(reg.task)
#> Error: Cannot combine stratification with groupingBelow we show how ResamplingSameOtherSizesCV can be used
instead:
ignore.cv <- mlr3resampling::ResamplingSameOtherSizesCV$new()
ignore.cv$param_set$values$ignore_subset <- TRUE
ignore.cv$instantiate(reg.task)
ignore.cv$instance$iteration.dt
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: full same 200 1 5, 6, 7, 8, 9,10,...
#> 2: full same 200 2 3, 4,11,12,13,14,...
#> 3: full same 200 3 1, 2,25,26,31,32,...
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 1, 2, 3, 4,11,12,... 1 200 1
#> 2: 1,2,5,6,7,8,... 1 200 2
#> 3: 3,4,5,6,7,8,... 1 200 3To use the above CV object with a learning algorithm in a benchmark
experiment, we need to use it as the resampling argument to
auto_tuner, as in the code below,
do_benchmark <- function(subtrain.valid.cv){
reg.learner.list <- list(
mlr3::LearnerRegrFeatureless$new())
if(requireNamespace("rpart")){
reg.learner.list$rpart <- mlr3::LearnerRegrRpart$new()
if(requireNamespace("mlr3tuning")){
rpart.learner <- mlr3::LearnerRegrRpart$new()
##mlr3tuningspaces::lts(rpart.learner)$param_set$values
rpart.learner$param_set$values$cp <- paradox::to_tune(1e-4, 0.1, log=TRUE)
reg.learner.list$rpart.tuned <- mlr3tuning::auto_tuner(
tuner = mlr3tuning::tnr("grid_search"), #mlr3tuning::TunerBatchGridSearch$new()
learner = rpart.learner,
resampling = subtrain.valid.cv,
measure = mlr3::msr("regr.mse"))
}
}
same.other.grid <- mlr3::benchmark_grid(
reg.task,
reg.learner.list,
same_other_sizes_cv)
lgr::get_logger("bbotk")$set_threshold("warn")
same.other.result <- mlr3::benchmark(
same.other.grid, store_models = TRUE)
}do_benchmark(mlr3::ResamplingCV$new())
#> Loading required namespace: mlr3tuning
#> Error: Cannot combine stratification with groupingThe error above is because ResamplingCV does not support
stratification and grouping. To fix that, we can use the code below:
ignore.cv <- mlr3resampling::ResamplingSameOtherSizesCV$new()
ignore.cv$param_set$values$ignore_subset <- TRUE
(same.other.result <- do_benchmark(ignore.cv))
#> <BenchmarkResult> of 108 rows with 3 resampling runs
#> nr task_id learner_id resampling_id iters warnings errors
#> 1 sin regr.featureless same_other_sizes_cv 36 0 0
#> 2 sin regr.rpart same_other_sizes_cv 36 0 0
#> 3 sin regr.rpart.tuned same_other_sizes_cv 36 0 0The output above shows that the benchmark worked. The code below plots the results.
same.other.score <- mlr3resampling::score(same.other.result)
same.other.score[1]
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: A all 200 1 1, 2,49,50,57,58,...
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 5, 6, 9,10,15,16,... 1 50 1
#> uhash nr task task_id
#> <char> <int> <list> <char>
#> 1: e21f7847-1ace-49b0-a407-c7219bae0470 1 <TaskRegr:sin> sin
#> learner learner_id
#> <list> <char>
#> 1: <LearnerRegrFeatureless:regr.featureless> regr.featureless
#> resampling resampling_id prediction_test regr.mse
#> <list> <char> <list> <num>
#> 1: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionRegr> 0.5814085
#> algorithm
#> <char>
#> 1: featureless
same.other.wide <- dcast(
same.other.score,
algorithm + test.subset + train.subsets ~ .,
list(mean, sd),
value.var="regr.mse")
if(require(ggplot2)){
ggplot()+
geom_segment(aes(
regr.mse_mean+regr.mse_sd, train.subsets,
xend=regr.mse_mean-regr.mse_sd, yend=train.subsets),
data=same.other.wide)+
geom_point(aes(
regr.mse_mean, train.subsets),
shape=1,
data=same.other.wide)+
facet_grid(algorithm ~ test.subset, labeller=label_both)
}
The plot above has different panels for rpart (without
tuning) and tuned (rpart with tuning of
cp).
Conclusions
mlr3resampling::ResamplingSameOtherSizesCV can be used
for model evaluation (train/test split):
- compare prediction accuracy of models trained on same/other/all
subsets (need to set column role
subset). - compare prediction accuracy of models trained on down-sampled
subsets (need to set param
sizes).
It can also be used for model training (subtrain/validation split):
- to learn regularization hyper-parameters, on a task with both
stratumandgrouproles (use is asresamplingargument ofauto_tuner).
Arizona trees data
The goal of this section is explain the differences between various column roles:
groupis used to designate observations which should stay together when splitting. In other words, two rows in the samegroupshould never appear in different sets.subsetdesignates a column whose values are each treated as a test set (the train data come from Same/Other/All subsets).
What is a group?
Below we load the data set.
data(AZtrees,package="mlr3resampling")
library(data.table)
AZdt <- data.table(AZtrees)
AZdt[1]
#> xcoord ycoord region3 region4 polygon y SAMPLE_1 SAMPLE_2
#> <num> <num> <char> <char> <fctr> <fctr> <int> <int>
#> 1: -111.6643 35.23736 NE NE 1 Not tree 3331 3919
#> SAMPLE_3 SAMPLE_4 SAMPLE_5 SAMPLE_6 SAMPLE_7 SAMPLE_8 SAMPLE_9 SAMPLE_10
#> <int> <int> <int> <int> <int> <int> <int> <int>
#> 1: 3957 4514 4700 4607 4420 4494 4139 3906
#> SAMPLE_11 SAMPLE_12 SAMPLE_13 SAMPLE_14 SAMPLE_15 SAMPLE_16 SAMPLE_17
#> <int> <int> <int> <int> <int> <int> <int>
#> 1: 14 -40 -71 125 21 25 10
#> SAMPLE_18 SAMPLE_19 SAMPLE_20 SAMPLE_21
#> <int> <int> <int> <int>
#> 1: -263 -324 -362 370Above we see one row of data. Below we see a scatterplot of the data:
- Every row is a labeled pixel.
- Every dot is plotted at the xcoord/ycoord (lat/long) position on a map around Flagstaff, AZ.
x.center <- -111.72
y.center <- 35.272
rect.size <- 0.01/2
x.min.max <- x.center+c(-1, 1)*rect.size
y.min.max <- y.center+c(-1, 1)*rect.size
rect.dt <- data.table(
xmin=x.min.max[1], xmax=x.min.max[2],
ymin=y.min.max[1], ymax=y.min.max[2])
if(require(ggplot2)){
tree.fill.scale <- scale_fill_manual(
values=c(Tree="black", "Not tree"="white"))
ggplot()+
theme_bw()+
tree.fill.scale+
geom_rect(aes(
xmin=xmin, xmax=xmax, ymin=ymin,ymax=ymax),
data=rect.dt,
fill="red",
linewidth=3,
color="red")+
geom_point(aes(
xcoord, ycoord, fill=y),
shape=21,
data=AZdt)+
coord_equal()
}
Note the red square in the plot above. Below we zoom into that square.
if(require(ggplot2)){
gg <- ggplot()+
theme_bw()+
tree.fill.scale+
geom_point(aes(
xcoord, ycoord, fill=y),
shape=21,
data=AZdt)+
coord_equal()+
scale_x_continuous(
limits=x.min.max)+
scale_y_continuous(
limits=y.min.max)
if(require(directlabels)){
gg <- gg+geom_dl(aes(
xcoord, ycoord, label=polygon),
data=AZdt,
method="smart.grid")
}
gg
}
#> Loading required package: directlabels
#> Warning: Removed 5927 rows containing missing values or values outside the scale range
#> (`geom_point()`).
#> Warning: Removed 5927 rows containing missing values or values outside the scale range
#> (`geom_dl()`).
In the plot above, we see that there are several groups of points, each with a black number. Each group of points comes from a single polygon (label drawn in GIS software), and the black number is the polygon ID number. So each polygon represents one label, either tree or not, and there are one or more points/pixels with that label inside each polygon.
A polygon is an example of a group. Each polygon results in one or more rows of training data (pixels), but since pixels in a given group were all labeled together, we would like to keep them together when splitting the data.
What is a subset?
Below we plot the same data, but this time colored by region.
##dput(RColorBrewer::brewer.pal(3,"Dark2"))
region.colors <- c(NW="#1B9E77", NE="#D95F02", S="#7570B3")
if(require(ggplot2)){
ggplot()+
theme_bw()+
tree.fill.scale+
scale_color_manual(
values=region.colors)+
geom_point(aes(
xcoord, ycoord, color=region3, fill=y),
shape=21,
data=AZdt)+
coord_equal()
}
We can see in the plot above that there are three values in the
region3 column: NE, NW, and S (different geographical
regions on the map which are well-separated). We would like to know if
it is possible to train on one region, and then accurately predict on
another region.
Cross-validation
First we create a task:
ctask <- mlr3::TaskClassif$new(
"AZtrees", AZdt, target="y")
ctask$col_roles$subset <- "region3"
ctask$col_roles$group <- "polygon"
ctask$col_roles$stratum <- "y"
ctask$col_roles$feature <- grep("SAMPLE",names(AZdt),value=TRUE)
str(ctask$col_roles)
#> List of 8
#> $ feature: chr [1:21] "SAMPLE_1" "SAMPLE_2" "SAMPLE_3" "SAMPLE_4" ...
#> $ target : chr "y"
#> $ name : chr(0)
#> $ order : chr(0)
#> $ stratum: chr "y"
#> $ group : chr "polygon"
#> $ weight : chr(0)
#> $ subset : chr "region3"Then we can instantiate the CV to see how it works (but usually you
do not need to instantiate, if you are using benchmark it
does it for you).
same.other.cv <- mlr3resampling::ResamplingSameOtherSizesCV$new()
same.other.cv$param_set$values$folds <- 3
same.other.cv$instantiate(ctask)
same.other.cv$instance$iteration.dt[, .(
train.subsets, test.fold, test.subset, n.train.groups,
train.rows=sapply(train, length))]
#> train.subsets test.fold test.subset n.train.groups train.rows
#> <char> <int> <char> <int> <int>
#> 1: all 1 NE 125 3108
#> 2: all 1 NW 125 3108
#> 3: all 1 S 125 3108
#> 4: all 2 NE 125 4325
#> 5: all 2 NW 125 4325
#> 6: all 2 S 125 4325
#> 7: all 3 NE 125 4479
#> 8: all 3 NW 125 4479
#> 9: all 3 S 125 4479
#> 10: other 1 NE 55 1934
#> 11: other 1 NW 104 1652
#> 12: other 1 S 91 2630
#> 13: other 2 NE 55 3550
#> 14: other 2 NW 104 3524
#> 15: other 2 S 91 1576
#> 16: other 3 NE 55 3500
#> 17: other 3 NW 104 3610
#> 18: other 3 S 91 1848
#> 19: same 1 NE 70 1174
#> 20: same 1 NW 21 1456
#> 21: same 1 S 34 478
#> 22: same 2 NE 70 775
#> 23: same 2 NW 21 801
#> 24: same 2 S 34 2749
#> 25: same 3 NE 70 979
#> 26: same 3 NW 21 869
#> 27: same 3 S 34 2631
#> train.subsets test.fold test.subset n.train.groups train.rowsThe table above has one row per train/test split for which
error/accuracy metrics will be computed. The n.train.groups
column is the number of polygons which are used in the train set, which
is defined as the intersection of the train subsets and the train folds.
To double check, below we compute the total number of groups/polygons
per subset/region, and the expected number of train groups/polygons.
AZdt[, .(
polygons=length(unique(polygon))
), by=region3][
, train.polygons := polygons*with(same.other.cv$param_set$values, (folds-1)/folds)
][]
#> region3 polygons train.polygons
#> <char> <int> <num>
#> 1: NE 105 70.00000
#> 2: NW 32 21.33333
#> 3: S 52 34.66667It is clear that the counts in the train.polygons column
above match the numbers in the previous table column
n.train.groups. To determine the number of rows of train
data, we can look at the train.rows column in the previous
table.
Benchmark and test error computation
Below we define the benchmark experiment.
same.other.cv <- mlr3resampling::ResamplingSameOtherSizesCV$new()
(learner.list <- list(
mlr3::LearnerClassifFeatureless$new()))
#> [[1]]
#> <LearnerClassifFeatureless:classif.featureless>: Featureless Classification Learner
#> * Model: -
#> * Parameters: method=mode
#> * Packages: mlr3
#> * Predict Types: [response], prob
#> * Feature Types: logical, integer, numeric, character, factor, ordered,
#> POSIXct
#> * Properties: featureless, importance, missings, multiclass,
#> selected_features, twoclass
if(requireNamespace("rpart")){
learner.list$rpart <- mlr3::LearnerClassifRpart$new()
}
for(learner.i in seq_along(learner.list)){
learner.list[[learner.i]]$predict_type <- "prob"
}
(bench.grid <- mlr3::benchmark_grid(ctask, learner.list, same.other.cv))
#> task learner resampling
#> <char> <char> <char>
#> 1: AZtrees classif.featureless same_other_sizes_cv
#> 2: AZtrees classif.rpart same_other_sizes_cvAbove we see one row per combination of task, learner, and resampling. Below we compute the benchmark result and test accuracy.
bench.result <- mlr3::benchmark(bench.grid)
measure.list <- mlr3::msrs(c("classif.acc","classif.auc"))
score.dt <- mlr3resampling::score(bench.result, measure.list)
score.dt[1]
#> test.subset train.subsets groups test.fold test
#> <char> <char> <int> <int> <list>
#> 1: NE all 125 1 123,124,125,126,127,128,...
#> train seed n.train.groups iteration
#> <list> <int> <int> <int>
#> 1: 1,2,3,4,5,6,... 1 125 1
#> uhash nr task task_id
#> <char> <int> <list> <char>
#> 1: 8adc2213-1912-44cf-92a8-6df707584c47 1 <TaskClassif:AZtrees> AZtrees
#> learner learner_id
#> <list> <char>
#> 1: <LearnerClassifFeatureless:classif.featureless> classif.featureless
#> resampling resampling_id prediction_test
#> <list> <char> <list>
#> 1: <ResamplingSameOtherSizesCV> same_other_sizes_cv <PredictionClassif>
#> classif.acc classif.auc algorithm
#> <num> <num> <char>
#> 1: 0.6576819 0.5 featurelessAbove we see one row of the result, for one train/test split. Below we plot the accuracy results.
score.long <- melt(
score.dt,
measure.vars=measure(variable, pattern="classif.(acc|auc)"))
if(require(ggplot2)){
ggplot()+
geom_point(aes(
value, train.subsets, color=algorithm),
data=score.long)+
facet_grid(test.subset ~ variable, labeller=label_both, scales="free")
}
Above we show one dot per train/test split, and below we take the mean/SD over folds.
score.wide <- dcast(
score.long,
algorithm + test.subset + train.subsets + variable ~ .,
list(mean, sd),
value.var="value")
if(require(ggplot2)){
ggplot()+
geom_point(aes(
value_mean, train.subsets, color=algorithm),
size=3,
fill="white",
shape=21,
data=score.wide)+
geom_segment(aes(
value_mean+value_sd, train.subsets,
color=algorithm,
linewidth=algorithm,
xend=value_mean-value_sd, yend=train.subsets),
data=score.wide)+
scale_linewidth_manual(values=c(featureless=2, rpart=1))+
facet_grid(test.subset ~ variable, labeller=label_both, scales="free")+
scale_x_continuous(
"Mean +/- SD of test accuracy/AUC over folds/splits")
}
The plot above shows an interesting pattern:
- For test subsets NE and NW, training on other subsets is less accurate than training on the same subset. Training on All subsets is no more accurate than training on the same subset. These results suggest that learnable patterns in other subsets are too different to be beneficial for predicting on these subsets.
- For test subset S, training on other subsets is slightly more accurate than training on the same subset, and training on all subsets is slightly more accurate still. These results suggest that the learnable pattern is similar enough in the other subsets so as to be beneficial for prediction in subset S.
Conclusion
Column roles group, stratum, and
subset may be used together, in the same task, in order to
perform a cross-validation experiment which captures the structure in
the data.
Session info
sessionInfo()
#> R version 4.4.1 (2024-06-14)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.1 LTS
#>
#> Matrix products: default
#> BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] directlabels_2024.4.16 mlr3resampling_2024.10.28
#> [3] mlr3_0.21.1 ggplot2_3.5.1
#> [5] data.table_1.16.2
#>
#> loaded via a namespace (and not attached):
#> [1] sass_0.4.9 utf8_1.2.4 future_1.34.0
#> [4] listenv_0.9.1 digest_0.6.37 magrittr_2.0.3
#> [7] evaluate_1.0.1 grid_4.4.1 fastmap_1.2.0
#> [10] jsonlite_1.8.9 backports_1.5.0 fansi_1.0.6
#> [13] scales_1.3.0 mlr3tuning_1.1.0 codetools_0.2-20
#> [16] mlr3measures_1.0.0 palmerpenguins_0.1.1 jquerylib_0.1.4
#> [19] cli_3.6.3 rlang_1.1.4 crayon_1.5.3
#> [22] parallelly_1.38.0 future.apply_1.11.3 munsell_0.5.1
#> [25] withr_3.0.2 cachem_1.1.0 tools_4.4.1
#> [28] parallel_4.4.1 uuid_1.2-1 checkmate_2.3.2
#> [31] colorspace_2.1-1 globals_0.16.3 bbotk_1.2.0
#> [34] buildtools_1.0.0 vctrs_0.6.5 R6_2.5.1
#> [37] rpart_4.1.23 lifecycle_1.0.4 mlr3misc_0.15.1
#> [40] pkgconfig_2.0.3 pillar_1.9.0 bslib_0.8.0
#> [43] gtable_0.3.6 glue_1.8.0 lgr_0.4.4
#> [46] paradox_1.0.1 xfun_0.48 tibble_3.2.1
#> [49] highr_0.11 sys_3.4.3 knitr_1.48
#> [52] farver_2.1.2 htmltools_0.5.8.1 rmarkdown_2.28
#> [55] maketools_1.3.1 labeling_0.4.3 compiler_4.4.1
#> [58] quadprog_1.5-8