# Same/Other/All resampler

The goal of this vignette is to explain the older resamplers: `ResamplingVariableSizeTrainCV` and `ResamplingSameOtherCV`, which output some data which are useful for visualizing the train/test splits. If you do not want to visualize the train/test splits, then it is recommended to instead use the newere resampler, `ResamplingSameOtherSizesCV` (see other vignette).

# Same/Other/All resampler

The goal of thie section is to explain how to quantify the extent to which it is possible to train on one data subset, and predict on another data subset. This kind of problem occurs frequently in many different problem domains:

• geography: can we train on one region (say Europe) and accurately predict on another? (North America)
• time series: can we train on one time period (2000) and accurately predict on another? (2001)
• personalization: can we train on one person (Alice) and accurately predict on another? (Bob)

The ideas are similar to my previous blog posts about how to do this in python and R. Below we explain how to use `mlr3resampling` for this purpose, in simulated regression and classification problems. To use this method in real data, the important sections to read below are named “Benchmark: computing test error,” which show how to create these cross-validation experiments using mlr3 code.

## Simulated regression problems

We begin by generating some data which can be used with regression algorithms. Assume there is a data set with some rows from one person, some rows from another,

``````N <- 300
library(data.table)
set.seed(1)
abs.x <- 2
reg.dt <- data.table(
x=runif(N, -abs.x, abs.x),
person=rep(1:2, each=0.5*N))
reg.pattern.list <- list(
easy=function(x, person)x^2,
impossible=function(x, person)(x^2+person*3)*(-1)^person)
reg.dt[, (yname) := f(x,person)+rnorm(N)][]
}
reg.dt
#>               x person      y_easy y_impossible
#>           <num>  <int>       <num>        <num>
#>   1: -0.9379653      1  1.32996609    -2.918082
#>   2: -0.5115044      1  0.24307692    -3.866062
#>   3:  0.2914135      1 -0.23314657    -3.837799
#>   4:  1.6328312      1  1.73677545    -7.221749
#>   5: -1.1932723      1 -0.06356159    -5.877792
#>  ---
#> 296:  0.7257701      2 -2.48130642     5.180948
#> 297: -1.6033236      2  1.20453459     9.604312
#> 298: -1.5243898      2  1.89966190     7.511988
#> 299: -1.7982414      2  3.47047566    11.035397
#> 300:  1.7170157      2  0.60541972    10.719685
``````

The table above shows some simulated data for two regression problems:

• easy problem has the same pattern for each person, so it is possible/easy to train on one person, and accurately predict on another.
• impossible problem has a different pattern for each person, so it is impossible to train on one person, and accurately predict on another.
• when adapting the code above to real data, the important part is the `mlr3::TaskRegr` line which tells mlr3 what data set to use, what is the target column, and what is the subset/stratum column.

### Static visualization of simulated data

First we reshape the data using the code below,

``````(reg.tall <- nc::capture_melt_single(
reg.dt,
value.name="y"))
#>           <num>  <int>     <char>       <num>
#>   1: -0.9379653      1       easy  1.32996609
#>   2: -0.5115044      1       easy  0.24307692
#>   3:  0.2914135      1       easy -0.23314657
#>   4:  1.6328312      1       easy  1.73677545
#>   5: -1.1932723      1       easy -0.06356159
#>  ---
#> 596:  0.7257701      2 impossible  5.18094849
#> 597: -1.6033236      2 impossible  9.60431191
#> 598: -1.5243898      2 impossible  7.51198770
#> 599: -1.7982414      2 impossible 11.03539747
#> 600:  1.7170157      2 impossible 10.71968480
``````

The table above is a more convenient form for the visualization which we create using the code below,

``````if(require(animint2)){
ggplot()+
geom_point(aes(
x, y),
data=reg.tall)+
facet_grid(
labeller=label_both,
space="free",
scales="free")+
scale_y_continuous(
breaks=seq(-100, 100, by=2))
}
#> Registered S3 methods overwritten by 'animint2':
#>   method                   from
#>   [.uneval                 ggplot2
#>   drawDetails.zeroGrob     ggplot2
#>   grid.draw.absoluteGrob   ggplot2
#>   grobHeight.absoluteGrob  ggplot2
#>   grobHeight.zeroGrob      ggplot2
#>   grobWidth.absoluteGrob   ggplot2
#>   grobWidth.zeroGrob       ggplot2
#>   grobX.absoluteGrob       ggplot2
#>   grobY.absoluteGrob       ggplot2
#>   heightDetails.titleGrob  ggplot2
#>   heightDetails.zeroGrob   ggplot2
#>   makeContext.dotstackGrob ggplot2
#>   print.element            ggplot2
#>   print.ggplot2_bins       ggplot2
#>   print.rel                ggplot2
#>   print.theme              ggplot2
#>   print.uneval             ggplot2
#>   widthDetails.titleGrob   ggplot2
#>   widthDetails.zeroGrob    ggplot2
#>
#> Attaching package: 'animint2'
#> The following objects are masked from 'package:ggplot2':
#>
#>     %+%, %+replace%, Coord, CoordCartesian, CoordFixed, CoordFlip,
#>     CoordMap, CoordPolar, CoordQuickmap, CoordTrans, Geom, GeomAbline,
#>     GeomAnnotationMap, GeomArea, GeomBar, GeomBlank, GeomContour,
#>     GeomCrossbar, GeomCurve, GeomCustomAnn, GeomDensity, GeomDensity2d,
#>     GeomDotplot, GeomErrorbar, GeomErrorbarh, GeomHex, GeomHline,
#>     GeomLabel, GeomLine, GeomLinerange, GeomLogticks, GeomMap,
#>     GeomPath, GeomPoint, GeomPointrange, GeomPolygon, GeomRaster,
#>     GeomRasterAnn, GeomRect, GeomRibbon, GeomRug, GeomSegment,
#>     GeomSmooth, GeomSpoke, GeomStep, GeomText, GeomTile, GeomViolin,
#>     GeomVline, Position, PositionDodge, PositionFill, PositionIdentity,
#>     PositionJitter, PositionJitterdodge, PositionNudge, PositionStack,
#>     Scale, ScaleContinuous, ScaleContinuousDate,
#>     ScaleContinuousDatetime, ScaleContinuousIdentity,
#>     ScaleContinuousPosition, ScaleDiscrete, ScaleDiscreteIdentity,
#>     ScaleDiscretePosition, Stat, StatBin, StatBin2d, StatBindot,
#>     StatBinhex, StatContour, StatCount, StatDensity, StatDensity2d,
#>     StatEcdf, StatEllipse, StatFunction, StatIdentity, StatQq,
#>     StatSmooth, StatSum, StatSummary, StatSummary2d, StatSummaryBin,
#>     StatSummaryHex, StatUnique, StatYdensity, aes, aes_, aes_all,
#>     aes_auto, aes_q, aes_string, annotate, annotation_custom,
#>     annotation_logticks, annotation_map, annotation_raster,
#>     as_labeller, autoplot, benchplot, borders, calc_element,
#>     continuous_scale, coord_cartesian, coord_equal, coord_fixed,
#>     coord_flip, coord_map, coord_munch, coord_polar, coord_quickmap,
#>     coord_trans, cut_interval, cut_number, cut_width, discrete_scale,
#>     draw_key_abline, draw_key_blank, draw_key_crossbar,
#>     draw_key_dotplot, draw_key_label, draw_key_path, draw_key_point,
#>     draw_key_pointrange, draw_key_polygon, draw_key_rect,
#>     draw_key_smooth, draw_key_text, draw_key_vline, draw_key_vpath,
#>     economics, economics_long, element_blank, element_grob,
#>     element_line, element_rect, element_text, expand_limits,
#>     facet_grid, facet_null, facet_wrap, fortify, geom_abline,
#>     geom_area, geom_bar, geom_bin2d, geom_blank, geom_contour,
#>     geom_count, geom_crossbar, geom_curve, geom_density,
#>     geom_density2d, geom_density_2d, geom_dotplot, geom_errorbar,
#>     geom_errorbarh, geom_freqpoly, geom_hex, geom_histogram,
#>     geom_hline, geom_jitter, geom_label, geom_line, geom_linerange,
#>     geom_map, geom_path, geom_point, geom_pointrange, geom_polygon,
#>     geom_qq, geom_raster, geom_rect, geom_ribbon, geom_rug,
#>     geom_segment, geom_smooth, geom_spoke, geom_step, geom_text,
#>     geom_tile, geom_violin, geom_vline, gg_dep, ggplot, ggplotGrob,
#>     ggplot_build, ggplot_gtable, ggsave, ggtitle, guide_colorbar,
#>     guide_colourbar, guide_legend, guides, is.Coord, is.facet,
#>     is.ggplot, is.theme, label_both, label_bquote, label_context,
#>     label_parsed, label_value, label_wrap_gen, labeller, labs,
#>     last_plot, layer, layer_data, layer_grob, layer_scales, lims,
#>     map_data, margin, mean_cl_boot, mean_cl_normal, mean_sdl, mean_se,
#>     median_hilow, position_dodge, position_fill, position_identity,
#>     position_jitter, position_jitterdodge, position_nudge,
#>     position_stack, presidential, qplot, quickplot, rel,
#>     remove_missing, resolution, scale_alpha, scale_alpha_continuous,
#>     scale_alpha_discrete, scale_alpha_identity, scale_alpha_manual,
#>     scale_color_brewer, scale_color_continuous, scale_color_discrete,
#>     scale_color_identity, scale_color_manual, scale_colour_brewer,
#>     scale_colour_continuous, scale_colour_date, scale_colour_datetime,
#>     scale_colour_discrete, scale_colour_distiller,
#>     scale_colour_identity, scale_colour_manual, scale_fill_brewer,
#>     scale_fill_continuous, scale_fill_date, scale_fill_datetime,
#>     scale_fill_hue, scale_fill_identity, scale_fill_manual,
#>     scale_linetype, scale_linetype_continuous, scale_linetype_discrete,
#>     scale_shape, scale_shape_continuous, scale_shape_discrete,
#>     scale_shape_identity, scale_shape_manual, scale_size,
#>     scale_size_area, scale_size_continuous, scale_size_date,
#>     scale_size_datetime, scale_size_discrete, scale_size_identity,
#>     scale_size_manual, scale_x_continuous, scale_x_date,
#>     scale_x_datetime, scale_x_discrete, scale_x_log10, scale_x_reverse,
#>     scale_x_sqrt, scale_y_continuous, scale_y_date, scale_y_datetime,
#>     scale_y_discrete, scale_y_log10, scale_y_reverse, scale_y_sqrt,
#>     should_stop, stat_bin, stat_bin2d, stat_bin_2d, stat_bin_hex,
#>     stat_binhex, stat_contour, stat_count, stat_density,
#>     stat_density2d, stat_density_2d, stat_ecdf, stat_ellipse,
#>     stat_function, stat_identity, stat_qq, stat_smooth, stat_spoke,
#>     stat_sum, stat_summary, stat_summary2d, stat_summary_2d,
#>     stat_summary_bin, stat_summary_hex, stat_unique, stat_ydensity,
#>     theme, theme_bw, theme_classic, theme_dark, theme_get, theme_gray,
#>     theme_grey, theme_light, theme_linedraw, theme_minimal,
#>     theme_replace, theme_set, theme_update, theme_void,
#>     transform_position, update_geom_defaults, update_labels,
#>     update_stat_defaults, waiver, xlab, xlim, ylab, ylim, zeroGrob
``````

In the simulated data above, we can see that

• for the easy pattern, it is the same for both people, so it should be possible/easy to train on one person, and accurately predict on another.
• for the impossible pattern, it is different for each person, so it should not be possible to train on one person, and accurately predict on another.

### Benchmark: computing test error

In the code below, we define a K-fold cross-validation experiment.

``````(reg_same_other <- mlr3resampling::ResamplingSameOtherCV\$new())
#> <ResamplingSameOtherCV> : Same versus Other Cross-Validation
#> * Iterations:
#> * Instantiated: FALSE
#> * Parameters:
#> List of 1
#>  \$ folds: int 3
``````

In the code below, we define two learners to compare,

``````(reg.learner.list <- list(
if(requireNamespace("rpart"))mlr3::LearnerRegrRpart\$new(),
mlr3::LearnerRegrFeatureless\$new()))
#> [[1]]
#> <LearnerRegrRpart:regr.rpart>: Regression Tree
#> * Model: -
#> * Parameters: xval=0
#> * Packages: mlr3, rpart
#> * Predict Types:  [response]
#> * Feature Types: logical, integer, numeric, factor, ordered
#> * Properties: importance, missings, selected_features, weights
#>
#> [[2]]
#> <LearnerRegrFeatureless:regr.featureless>: Featureless Regression Learner
#> * Model: -
#> * Parameters: robust=FALSE
#> * Packages: mlr3, stats
#> * Predict Types:  [response], se
#> * Feature Types: logical, integer, numeric, character, factor, ordered,
#>   POSIXct
#> * Properties: featureless, importance, missings, selected_features
``````

In the code below, we define the benchmark grid, which is all combinations of tasks (easy and impossible), learners (rpart and featureless), and the one resampling method.

``````(reg.bench.grid <- mlr3::benchmark_grid(
reg.learner.list,
reg_same_other))
#>        <char>           <char>        <char>
#> 1:       easy       regr.rpart same_other_cv
#> 2:       easy regr.featureless same_other_cv
#> 3: impossible       regr.rpart same_other_cv
#> 4: impossible regr.featureless same_other_cv
``````

In the code below, we execute the benchmark experiment (in parallel using the multisession future plan).

``````if(FALSE){#for CRAN.
if(require(future))plan("multisession")
}
if(require(lgr))get_logger("mlr3")\$set_threshold("warn")
#>
#> Attaching package: 'lgr'
#> The following object is masked from 'package:ggplot2':
#>
#>     Layout
(reg.bench.result <- mlr3::benchmark(
reg.bench.grid, store_models = TRUE))
#> <BenchmarkResult> of 72 rows with 4 resampling runs
#>  nr    task_id       learner_id resampling_id iters warnings errors
#>   1       easy       regr.rpart same_other_cv    18        0      0
#>   2       easy regr.featureless same_other_cv    18        0      0
#>   3 impossible       regr.rpart same_other_cv    18        0      0
#>   4 impossible regr.featureless same_other_cv    18        0      0
``````

The code below computes the test error for each split,

``````reg.bench.score <- mlr3resampling::score(reg.bench.result)
reg.bench.score[1]
#>    train.subsets test.fold test.subset person iteration                  test
#>           <char>     <int>       <int>  <int>     <int>                <list>
#> 1:           all         1           1      1         1  1, 3, 5, 6,12,13,...
#>                    train                                uhash    nr
#>                   <list>                               <char> <int>
#> 1:  4, 7, 9,10,18,20,... e839f8b2-a366-4406-abe4-627c12967073     1
#>             <list>  <char>                        <list>     <char>
#> 1: <TaskRegr:easy>    easy <LearnerRegrRpart:regr.rpart> regr.rpart
#>                 resampling resampling_id       prediction regr.mse algorithm
#>                     <list>        <char>           <list>    <num>    <char>
#> 1: <ResamplingSameOtherCV> same_other_cv <PredictionRegr> 1.638015     rpart
``````

The code below visualizes the resulting test accuracy numbers.

``````if(require(animint2)){
ggplot()+
scale_x_log10()+
geom_point(aes(
regr.mse, train.subsets, color=algorithm),
shape=1,
data=reg.bench.score)+
facet_grid(
labeller=label_both,
scales="free")
}
``````

It is clear from the plot above that

• for the easy task, training on same is just as good as all or other subsets. rpart has much lower test error than featureless, in all three train subsets.
• for the impossible task, the least test error is using rpart with same train subsets; featureless with same train subsets is next best; training on all is substantially worse (for both featureless and rpart); training on other is even worse (patterns in the two people are completely different).
• in a real data task, training on other will most likely not be quite as bad as in the impossible task above, but also not as good as in the easy task.

### Interactive visualization of data, test error, and splits

The code below can be used to create an interactive data visualization which allows exploring how different functions are learned during different splits.

``````inst <- reg.bench.score\$resampling[[1]]\$instance
rect.expand <- 0.2
grid.dt <- data.table(x=seq(-abs.x, abs.x, l=101), y=0)
pred.dt.list <- list()
point.dt.list <- list()
for(score.i in 1:nrow(reg.bench.score)){
reg.bench.row <- reg.bench.score[score.i]
reg.bench.row\$resampling[[1]]\$instance\$id.dt)
set.ids <- data.table(
set.name=c("test","train")
)[
, data.table(row_id=reg.bench.row[[set.name]][[1]])
, by=set.name]
i.points <- set.ids[
][
is.na(set.name), set.name := "unused"
]
point.dt.list[[score.i]] <- data.table(
i.points)
i.learner <- reg.bench.row\$learner[[1]]
pred.dt.list[[score.i]] <- data.table(
reg.bench.row[, .(
)],
as.data.table(
)[, .(x=grid.dt\$x, y=response)]
)
}
(pred.dt <- rbindlist(pred.dt.list))
#>          task_id iteration   algorithm     x        y
#>           <char>     <int>      <char> <num>    <num>
#>    1:       easy         1       rpart -2.00 3.557968
#>    2:       easy         1       rpart -1.96 3.557968
#>    3:       easy         1       rpart -1.92 3.557968
#>    4:       easy         1       rpart -1.88 3.557968
#>    5:       easy         1       rpart -1.84 3.557968
#>   ---
#> 7268: impossible        18 featureless  1.84 7.204232
#> 7269: impossible        18 featureless  1.88 7.204232
#> 7270: impossible        18 featureless  1.92 7.204232
#> 7271: impossible        18 featureless  1.96 7.204232
#> 7272: impossible        18 featureless  2.00 7.204232
(point.dt <- rbindlist(point.dt.list))
#>           task_id iteration set.name row_id           y          x  fold person
#>            <char>     <int>   <char>  <int>       <num>      <num> <int>  <int>
#>     1:       easy         1     test      1  1.32996609 -0.9379653     1      1
#>     2:       easy         1    train      2  0.24307692 -0.5115044     3      1
#>     3:       easy         1     test      3 -0.23314657  0.2914135     1      1
#>     4:       easy         1    train      4  1.73677545  1.6328312     2      1
#>     5:       easy         1     test      5 -0.06356159 -1.1932723     1      1
#>    ---
#> 21596: impossible        18    train    296  5.18094849  0.7257701     1      2
#> 21597: impossible        18    train    297  9.60431191 -1.6033236     1      2
#> 21598: impossible        18     test    298  7.51198770 -1.5243898     3      2
#> 21599: impossible        18    train    299 11.03539747 -1.7982414     1      2
#> 21600: impossible        18     test    300 10.71968480  1.7170157     3      2
#>        subset display_row
#>         <int>       <int>
#>     1:      1           1
#>     2:      1         101
#>     3:      1           2
#>     4:      1          51
#>     5:      1           3
#>    ---
#> 21596:      2         198
#> 21597:      2         199
#> 21598:      2         299
#> 21599:      2         200
#> 21600:      2         300
set.colors <- c(
train="#1B9E77",
test="#D95F02",
unused="white")
algo.colors <- c(
featureless="blue",
rpart="red")
make_person_subset <- function(DT){
DT[, "person/subset" := person]
}
make_person_subset(point.dt)
make_person_subset(reg.bench.score)

if(require(animint2)){
viz <- animint(
title="Train/predict on subsets, regression",
pred=ggplot()+
ggtitle("Predictions for selected train/test split")+
theme_animint(height=400)+
scale_fill_manual(values=set.colors)+
geom_point(aes(
x, y, fill=set.name),
showSelected="iteration",
size=3,
shape=21,
data=point.dt)+
scale_color_manual(values=algo.colors)+
geom_line(aes(
x, y, color=algorithm, subset=paste(algorithm, iteration)),
showSelected="iteration",
data=pred.dt)+
facet_grid(
labeller=label_both,
space="free",
scales="free")+
scale_y_continuous(
breaks=seq(-100, 100, by=2)),
err=ggplot()+
ggtitle("Test error for each split")+
theme_animint(height=400)+
scale_y_log10(
"Mean squared error on test set")+
scale_fill_manual(values=algo.colors)+
scale_x_discrete(
"People/subsets in train set")+
geom_point(aes(
train.subsets, regr.mse, fill=algorithm),
shape=1,
size=5,
stroke=2,
color="black",
color_off=NA,
clickSelects="iteration",
data=reg.bench.score)+
facet_grid(
labeller=label_both,
scales="free"),
diagram=ggplot()+
ggtitle("Select train/test split")+
theme_bw()+
theme_animint(height=300)+
facet_grid(
. ~ train.subsets,
scales="free",
space="free")+
scale_size_manual(values=c(subset=3, fold=1))+
scale_color_manual(values=c(subset="orange", fold="grey50"))+
geom_rect(aes(
xmin=-Inf, xmax=Inf,
color=rows,
size=rows,
ymin=display_row, ymax=display_end),
fill=NA,
data=inst\$viz.rect.dt)+
scale_fill_manual(values=set.colors)+
geom_rect(aes(
xmin=iteration-rect.expand, ymin=display_row,
xmax=iteration+rect.expand, ymax=display_end,
fill=set.name),
clickSelects="iteration",
data=inst\$viz.set.dt)+
geom_text(aes(
ifelse(rows=="subset", Inf, -Inf),
(display_row+display_end)/2,
hjust=ifelse(rows=="subset", 1, 0),
label=paste0(rows, "=", ifelse(rows=="subset", subset, fold))),
data=data.table(train.name="same", inst\$viz.rect.dt))+
scale_x_continuous(
"Split number / cross-validation iteration")+
scale_y_continuous(
"Row number"),
source="https://github.com/tdhock/mlr3resampling/blob/main/vignettes/ResamplingSameOtherCV.Rmd")
viz
}
``````
, and

``````if(FALSE){
animint2pages(viz, "2023-12-13-train-predict-subsets-regression")
}
``````

If you are viewing this in an installed package or on CRAN, then there will be no data viz on this page, but you can view it on: https://tdhock.github.io/2023-12-13-train-predict-subsets-regression/

## Simulated classification problems

The previous section investigated a simulated regression problem, whereas in this section we simulate a binary classification problem. Assume there is a data set with some rows from one person, some rows from another,

``````N <- 200
library(data.table)
(full.dt <- data.table(
label=factor(rep(c("spam","not spam"), l=N)),
person=rep(1:2, each=0.5*N)
)[, signal := ifelse(label=="not spam", 0, 3)][])
#>         label person signal
#>        <fctr>  <int>  <num>
#>   1:     spam      1      3
#>   2: not spam      1      0
#>   3:     spam      1      3
#>   4: not spam      1      0
#>   5:     spam      1      3
#>  ---
#> 196: not spam      2      0
#> 197:     spam      2      3
#> 198: not spam      2      0
#> 199:     spam      2      3
#> 200: not spam      2      0
``````

Above each row has an person ID between 1 and 2. We can imagine a spam filtering system, that has training data for multiple people (here just two). Each row in the table above represents a message which has been labeled as spam or not, by one of the two people. Can we train on one person, and accurately predict on the other person? To do that we will need some features, which we generate/simulate below:

``````set.seed(1)
n.people <- length(unique(full.dt\$person))
for(person.i in 1:n.people){
use.signal.vec <- list(
easy=rep(if(person.i==1)TRUE else FALSE, N),
impossible=full.dt\$person==person.i)
full.dt[
use.signal, signal, 0
)+rnorm(N)][]
}
}
full.dt
#>         label person signal    x1_easy x1_impossible    x2_easy x2_impossible
#>        <fctr>  <int>  <num>      <num>         <num>      <num>         <num>
#>   1:     spam      1      3  2.3735462     3.4094018  1.0744410    -0.3410670
#>   2: not spam      1      0  0.1836433     1.6888733  1.8956548     1.5024245
#>   3:     spam      1      3  2.1643714     4.5865884 -0.6029973     0.5283077
#>   4: not spam      1      0  1.5952808    -0.3309078 -0.3908678     0.5421914
#>   5:     spam      1      3  3.3295078     0.7147645 -0.4162220    -0.1366734
#>  ---
#> 196: not spam      2      0 -1.0479844    -0.9243128  0.7682782    -1.0293917
#> 197:     spam      2      3  4.4411577     1.5929138 -0.8161606     2.9890743
#> 198: not spam      2      0 -1.0158475     0.0450106 -0.4361069    -1.2249912
#> 199:     spam      2      3  3.4119747    -0.7151284  0.9047050     0.4038886
#> 200: not spam      2      0 -0.3810761     0.8652231 -0.7630863     1.1691226
``````

In the table above, there are two sets of two features:

• For easy features, one is correlated with the label (`x1_easy`), and one is random noise (`x2_easy`), so the algorithm just needs to learn to ignore the noise feature, and concentrate on the signal feature. That should be possible given data from either person (same signal in each person).
• Each impossible feature is correlated with the label (when feature number same as person number), or is just noise (when person number different from feature number). So if the algorithm has access to the correct person (same as test, say person 2), then it needs to learn to use the corresponding feature `x2_impossible`. But if the algorithm does not have access to that person, then the best it can do is same as featureless (predict most frequent class label in train data).

### Static visualization of simulated data

Below we reshape the data to a table which is more suitable for visualization:

``````(scatter.dt <- nc::capture_melt_multiple(
full.dt,
column="x[12]",
"_",
#>         label person signal    task_id         x1         x2
#>        <fctr>  <int>  <num>     <char>      <num>      <num>
#>   1:     spam      1      3       easy  2.3735462  1.0744410
#>   2: not spam      1      0       easy  0.1836433  1.8956548
#>   3:     spam      1      3       easy  2.1643714 -0.6029973
#>   4: not spam      1      0       easy  1.5952808 -0.3908678
#>   5:     spam      1      3       easy  3.3295078 -0.4162220
#>  ---
#> 396: not spam      2      0 impossible -0.9243128 -1.0293917
#> 397:     spam      2      3 impossible  1.5929138  2.9890743
#> 398: not spam      2      0 impossible  0.0450106 -1.2249912
#> 399:     spam      2      3 impossible -0.7151284  0.4038886
#> 400: not spam      2      0 impossible  0.8652231  1.1691226
``````

Below we visualize the pattern for each person and feature type:

``````if(require(animint2)){
ggplot()+
geom_point(aes(
x1, x2, color=label),
shape=1,
data=scatter.dt)+
facet_grid(
labeller=label_both)
}
``````

In the plot above, it is apparent that

• for easy features (left), the two label classes differ in x1 values for both people. So it should be possible/easy to train on person 1, and predict accurately on person 2.
• for impossible features (right), the two people have different label patterns. For person 1, the two label classes differ in x1 values, whereas for person 2, the two label classes differ in x2 values. So it should be impossible to train on person 1, and predict accurately on person 2.

### Benchmark: computing test error

We use the code below to create a list of classification tasks, for use in the mlr3 framework.

``````class.task.list <- list()
}
#> \$easy
#> * Target: label
#> * Properties: twoclass, strata
#> * Features (2):
#>   - dbl (2): x1_easy, x2_easy
#> * Strata: person, label
#>
#> \$impossible
#> * Target: label
#> * Properties: twoclass, strata
#> * Features (2):
#>   - dbl (2): x1_impossible, x2_impossible
#> * Strata: person, label
``````

Note in the code above that person is assigned roles subset and stratum, whereas label is assigned roles target and stratum. When adapting the code above to real data, the important part is the `mlr3::TaskClassif` line which tells mlr3 what data set to use, and what columns should be used for target/subset/stratum.

The code below is used to define a K-fold cross-validation experiment,

``````(class_same_other <- mlr3resampling::ResamplingSameOtherCV\$new())
#> <ResamplingSameOtherCV> : Same versus Other Cross-Validation
#> * Iterations:
#> * Instantiated: FALSE
#> * Parameters:
#> List of 1
#>  \$ folds: int 3
``````

The code below is used to define the learning algorithms to test,

``````(class.learner.list <- list(
if(requireNamespace("rpart"))mlr3::LearnerClassifRpart\$new(),
mlr3::LearnerClassifFeatureless\$new()))
#> [[1]]
#> <LearnerClassifRpart:classif.rpart>: Classification Tree
#> * Model: -
#> * Parameters: xval=0
#> * Packages: mlr3, rpart
#> * Predict Types:  [response], prob
#> * Feature Types: logical, integer, numeric, factor, ordered
#> * Properties: importance, missings, multiclass, selected_features,
#>   twoclass, weights
#>
#> [[2]]
#> <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
``````

The code below defines the grid of tasks, learners, and resamplings.

``````(class.bench.grid <- mlr3::benchmark_grid(
class.learner.list,
class_same_other))
#>        <char>              <char>        <char>
#> 1:       easy       classif.rpart same_other_cv
#> 2:       easy classif.featureless same_other_cv
#> 3: impossible       classif.rpart same_other_cv
#> 4: impossible classif.featureless same_other_cv
``````

The code below runs the benchmark experiment grid. Note that each iteration can be parallelized by declaring a future plan.

``````if(FALSE){
if(require(future))plan("multisession")
}
if(require(lgr))get_logger("mlr3")\$set_threshold("warn")
(class.bench.result <- mlr3::benchmark(
class.bench.grid, store_models = TRUE))
#> <BenchmarkResult> of 72 rows with 4 resampling runs
#>  nr    task_id          learner_id resampling_id iters warnings errors
#>   1       easy       classif.rpart same_other_cv    18        0      0
#>   2       easy classif.featureless same_other_cv    18        0      0
#>   3 impossible       classif.rpart same_other_cv    18        0      0
#>   4 impossible classif.featureless same_other_cv    18        0      0
``````

Below we compute scores (test error) for each resampling iteration, and show the first row of the result.

``````class.bench.score <- mlr3resampling::score(class.bench.result)
class.bench.score[1]
#>    train.subsets test.fold test.subset person iteration                  test
#>           <char>     <int>       <int>  <int>     <int>                <list>
#> 1:           all         1           1      1         1  1, 2, 8,11,12,18,...
#>                    train                                uhash    nr
#>                   <list>                               <char> <int>
#> 1:  3, 4, 5, 6, 9,10,... feb4f442-9d38-4b1b-82a6-451c8f71e02b     1
#>                <list>  <char>                              <list>        <char>
#> 1: <TaskClassif:easy>    easy <LearnerClassifRpart:classif.rpart> classif.rpart
#>                 resampling resampling_id          prediction classif.ce
#>                     <list>        <char>              <list>      <num>
#> 1: <ResamplingSameOtherCV> same_other_cv <PredictionClassif> 0.08823529
#>    algorithm
#>       <char>
#> 1:     rpart
``````

Finally we plot the test error values below.

``````if(require(animint2)){
ggplot()+
geom_point(aes(
classif.ce, train.subsets, color=algorithm),
shape=1,
data=class.bench.score)+
facet_grid(
labeller=label_both,
scales="free")
}
``````

It is clear from the plot above that

• for the easy task, training on same is just as good as all or other subsets.
• for the impossible task, we must train on same subset for minimal test error; training on all is almost as good, because the pattern in person 1 is orthogonal to person 2; training on other is just as bad as featureless, because patterns are different.
• in a real data task, training on other will most likely not be quite as bad as in the impossible task above, but also not as good as in the easy task.

### Interactive visualization of data, test error, and splits

The code below can be used to create an interactive data visualization which allows exploring how different functions are learned during different splits.

``````inst <- class.bench.score\$resampling[[1]]\$instance
rect.expand <- 0.2
grid.value.dt <- scatter.dt[
, lapply(.SD, function(x)do.call(seq, c(as.list(range(x)), l=21)))
, .SDcols=c("x1","x2")]
grid.class.dt <- data.table(
label=full.dt\$label[1],
do.call(
CJ, grid.value.dt
)
)
class.pred.dt.list <- list()
class.point.dt.list <- list()
for(score.i in 1:nrow(class.bench.score)){
class.bench.row <- class.bench.score[score.i]
class.bench.row\$resampling[[1]]\$instance\$id.dt)
set.ids <- data.table(
set.name=c("test","train")
)[
, data.table(row_id=class.bench.row[[set.name]][[1]])
, by=set.name]
i.points <- set.ids[
][
is.na(set.name), set.name := "unused"
][]
class.point.dt.list[[score.i]] <- data.table(
i.points)
if(class.bench.row\$algorithm!="featureless"){
i.learner <- class.bench.row\$learner[[1]]
i.learner\$predict_type <- "prob"
"grid", grid.class.dt, target="label")
pred.grid <- as.data.table(
)[, data.table(grid.class.dt, prob.spam)]
names(pred.grid)[2:3] <- c("x1","x2")
pred.wide <- dcast(pred.grid, x1 ~ x2, value.var="prob.spam")
prob.mat <- as.matrix(pred.wide[,-1])
contour.list <- contourLines(
grid.value.dt\$x1, grid.value.dt\$x2, prob.mat, levels=0.5)
class.pred.dt.list[[score.i]] <- data.table(
class.bench.row[, .(
)],
data.table(contour.i=seq_along(contour.list))[, {
do.call(data.table, contour.list[[contour.i]])[, .(level, x1=x, x2=y)]
}, by=contour.i]
)
}
}
(class.pred.dt <- rbindlist(class.pred.dt.list))
#>         task_id iteration algorithm contour.i level       x1        x2
#>          <char>     <int>    <char>     <int> <num>    <num>     <num>
#>   1:       easy         1     rpart         1   0.5 1.856156 -3.008049
#>   2:       easy         1     rpart         1   0.5 1.856156 -2.606579
#>   3:       easy         1     rpart         1   0.5 1.856156 -2.205109
#>   4:       easy         1     rpart         1   0.5 1.856156 -1.803639
#>   5:       easy         1     rpart         1   0.5 1.856156 -1.402169
#>  ---
#> 766: impossible        18     rpart         1   0.5 3.743510  1.225096
#> 767: impossible        18     rpart         1   0.5 4.158037  1.225096
#> 768: impossible        18     rpart         1   0.5 4.572564  1.225096
#> 769: impossible        18     rpart         1   0.5 4.987091  1.225096
#> 770: impossible        18     rpart         1   0.5 5.401618  1.225096
(class.point.dt <- rbindlist(class.point.dt.list))
#>           task_id iteration set.name row_id    label         x1         x2
#>            <char>     <int>   <char>  <int>   <fctr>      <num>      <num>
#>     1:       easy         1     test      1     spam  2.3735462  1.0744410
#>     2:       easy         1     test      2 not spam  0.1836433  1.8956548
#>     3:       easy         1    train      3     spam  2.1643714 -0.6029973
#>     4:       easy         1    train      4 not spam  1.5952808 -0.3908678
#>     5:       easy         1    train      5     spam  3.3295078 -0.4162220
#>    ---
#> 14396: impossible        18    train    196 not spam -0.9243128 -1.0293917
#> 14397: impossible        18    train    197     spam  1.5929138  2.9890743
#> 14398: impossible        18    train    198 not spam  0.0450106 -1.2249912
#> 14399: impossible        18    train    199     spam -0.7151284  0.4038886
#> 14400: impossible        18    train    200 not spam  0.8652231  1.1691226
#>         fold person subset display_row
#>        <int>  <int>  <int>       <int>
#>     1:     1      1      1           1
#>     2:     1      1      1           2
#>     3:     2      1      1          35
#>     4:     2      1      1          36
#>     5:     2      1      1          37
#>    ---
#> 14396:     2      2      2         166
#> 14397:     2      2      2         167
#> 14398:     1      2      2         133
#> 14399:     1      2      2         134
#> 14400:     2      2      2         168

set.colors <- c(
train="#1B9E77",
test="#D95F02",
unused="white")
algo.colors <- c(
featureless="blue",
rpart="red")
make_person_subset <- function(DT){
DT[, "person/subset" := person]
}
make_person_subset(class.point.dt)
make_person_subset(class.bench.score)
if(require(animint2)){
viz <- animint(
title="Train/predict on subsets, classification",
pred=ggplot()+
ggtitle("Predictions for selected train/test split")+
theme_animint(height=400)+
scale_fill_manual(values=set.colors)+
scale_color_manual(values=c(spam="black","not spam"="white"))+
geom_point(aes(
x1, x2, color=label, fill=set.name),
showSelected="iteration",
size=3,
stroke=2,
shape=21,
data=class.point.dt)+
geom_path(aes(
x1, x2,
subset=paste(algorithm, iteration, contour.i)),
showSelected=c("iteration","algorithm"),
color=algo.colors[["rpart"]],
data=class.pred.dt)+
facet_grid(
labeller=label_both,
space="free",
scales="free")+
scale_y_continuous(
breaks=seq(-100, 100, by=2)),
err=ggplot()+
ggtitle("Test error for each split")+
theme_animint(height=400)+
theme(panel.margin=grid::unit(1, "lines"))+
scale_y_continuous(
"Classification error on test set",
breaks=seq(0, 1, by=0.25))+
scale_fill_manual(values=algo.colors)+
scale_x_discrete(
"People/subsets in train set")+
geom_hline(aes(
yintercept=yint),
data=data.table(yint=0.5),
color="grey50")+
geom_point(aes(
train.subsets, classif.ce, fill=algorithm),
shape=1,
size=5,
stroke=2,
color="black",
color_off=NA,
clickSelects="iteration",
data=class.bench.score)+
facet_grid(
labeller=label_both),
diagram=ggplot()+
ggtitle("Select train/test split")+
theme_bw()+
theme_animint(height=300)+
facet_grid(
. ~ train.subsets,
scales="free",
space="free")+
scale_size_manual(values=c(subset=3, fold=1))+
scale_color_manual(values=c(subset="orange", fold="grey50"))+
geom_rect(aes(
xmin=-Inf, xmax=Inf,
color=rows,
size=rows,
ymin=display_row, ymax=display_end),
fill=NA,
data=inst\$viz.rect.dt)+
scale_fill_manual(values=set.colors)+
geom_rect(aes(
xmin=iteration-rect.expand, ymin=display_row,
xmax=iteration+rect.expand, ymax=display_end,
fill=set.name),
clickSelects="iteration",
data=inst\$viz.set.dt)+
geom_text(aes(
ifelse(rows=="subset", Inf, -Inf),
(display_row+display_end)/2,
hjust=ifelse(rows=="subset", 1, 0),
label=paste0(rows, "=", ifelse(rows=="subset", subset, fold))),
data=data.table(train.name="same", inst\$viz.rect.dt))+
scale_x_continuous(
"Split number / cross-validation iteration")+
scale_y_continuous(
"Row number"),
source="https://github.com/tdhock/mlr3resampling/blob/main/vignettes/ResamplingSameOtherCV.Rmd")
viz
}
``````

``````if(FALSE){
animint2pages(viz, "2023-12-13-train-predict-subsets-classification")
}
``````

If you are viewing this in an installed package or on CRAN, then there will be no data viz on this page, but you can view it on: https://tdhock.github.io/2023-12-13-train-predict-subsets-classification/

## Conclusion

In this section we have shown how to use mlr3resampling for comparing test error of models trained on same/all/other subsets.

# Variable size train resampler

The goal of this section is to explain how to `ResamplingVariableSizeTrainCV`, which can be used to determine how many train data are necessary to provide accurate predictions on a given test set.

## Simulated regression problems

The code below creates data for simulated regression problems. First we define a vector of input values,

``````N <- 300
abs.x <- 10
set.seed(1)
x.vec <- runif(N, -abs.x, abs.x)
str(x.vec)
#>  num [1:300] -4.69 -2.56 1.46 8.16 -5.97 ...
``````

Below we define a list of two true regression functions (tasks in mlr3 terminology) for our simulated data,

``````reg.pattern.list <- list(
sin=sin,
constant=function(x)0)
``````

The constant function represents a regression problem which can be solved by always predicting the mean value of outputs (featureless is the best possible learning algorithm). The sin function will be used to generate data with a non-linear pattern that will need to be learned. Below we use a for loop over these two functions/tasks, to simulate the data which will be used as input to the learning algorithms:

``````library(data.table)
reg.data.list <- list()
x=x.vec,
y = f(x.vec)+rnorm(N,sd=0.5))
)
}
(reg.data <- rbindlist(reg.data.list))
#>        <char>     <num>      <num>
#>   1:      sin -4.689827  1.2248390
#>   2:      sin -2.557522 -0.5607042
#>   3:      sin  1.457067  0.8345056
#>   4:      sin  8.164156  0.4875994
#>   5:      sin -5.966361 -0.4321800
#>  ---
#> 596: constant  3.628850 -0.6728968
#> 597: constant -8.016618  0.5168327
#> 598: constant -7.621949 -0.4058882
#> 599: constant -8.991207  0.9008627
#> 600: constant  8.585078  0.8857710
``````

In the table above, the input is x, and the output is y. Below we visualize these data, with one task in each facet/panel:

``````if(require(animint2)){
ggplot()+
geom_point(aes(
x, y),
data=reg.data)+
}
``````

In the plot above we can see two different simulated data sets (constant and sin). Note that the code above used the `animint2` package, which provides interactive extensions to the static graphics of the `ggplot2` package (see below section Interactive data viz).

### Visualizing instance table

In the code below, we define a K-fold cross-validation experiment, with K=3 folds.

``````reg_size_cv <- mlr3resampling::ResamplingVariableSizeTrainCV\$new()
reg_size_cv\$param_set\$values\$train_sizes <- 6
reg_size_cv
#> <ResamplingVariableSizeTrainCV> : Cross-Validation with variable size train sets
#> * Iterations:
#> * Instantiated: FALSE
#> * Parameters:
#> List of 4
#>  \$ folds         : int 3
#>  \$ min_train_data: int 10
#>  \$ random_seeds  : int 3
#>  \$ train_sizes   : int 6
``````

In the output above we can see the parameters of the resampling object, all of which should be integer scalars:

• `folds` is the number of cross-validation folds.
• `min_train_data` is the minimum number of train data to consider.
• `random_seeds` is the number of random seeds, each of which determines a different random ordering of the train data. The random ordering determines which data are included in small train set sizes.
• `train_sizes` is the number of train set sizes, evenly spaced on a log scale, from `min_train_data` to the max number of train data (determined by `folds`).

Below we instantiate the resampling on one of the tasks:

``````reg_size_cv\$instantiate(reg.task.list[["sin"]])
reg_size_cv\$instance
#> \$iteration.dt
#>     test.fold  seed small_stratum_size train_size_i train_size
#>         <int> <int>              <int>        <int>      <int>
#>  1:         1     1                 10            1         10
#>  2:         1     1                 18            2         18
#>  3:         1     1                 33            3         33
#>  4:         1     1                 60            4         60
#>  5:         1     1                110            5        110
#>  6:         1     1                200            6        200
#>  7:         1     2                 10            1         10
#>  8:         1     2                 18            2         18
#>  9:         1     2                 33            3         33
#> 10:         1     2                 60            4         60
#> 11:         1     2                110            5        110
#> 12:         1     2                200            6        200
#> 13:         1     3                 10            1         10
#> 14:         1     3                 18            2         18
#> 15:         1     3                 33            3         33
#> 16:         1     3                 60            4         60
#> 17:         1     3                110            5        110
#> 18:         1     3                200            6        200
#> 19:         2     1                 10            1         10
#> 20:         2     1                 18            2         18
#> 21:         2     1                 33            3         33
#> 22:         2     1                 60            4         60
#> 23:         2     1                110            5        110
#> 24:         2     1                200            6        200
#> 25:         2     2                 10            1         10
#> 26:         2     2                 18            2         18
#> 27:         2     2                 33            3         33
#> 28:         2     2                 60            4         60
#> 29:         2     2                110            5        110
#> 30:         2     2                200            6        200
#> 31:         2     3                 10            1         10
#> 32:         2     3                 18            2         18
#> 33:         2     3                 33            3         33
#> 34:         2     3                 60            4         60
#> 35:         2     3                110            5        110
#> 36:         2     3                200            6        200
#> 37:         3     1                 10            1         10
#> 38:         3     1                 18            2         18
#> 39:         3     1                 33            3         33
#> 40:         3     1                 60            4         60
#> 41:         3     1                110            5        110
#> 42:         3     1                200            6        200
#> 43:         3     2                 10            1         10
#> 44:         3     2                 18            2         18
#> 45:         3     2                 33            3         33
#> 46:         3     2                 60            4         60
#> 47:         3     2                110            5        110
#> 48:         3     2                200            6        200
#> 49:         3     3                 10            1         10
#> 50:         3     3                 18            2         18
#> 51:         3     3                 33            3         33
#> 52:         3     3                 60            4         60
#> 53:         3     3                110            5        110
#> 54:         3     3                200            6        200
#>     test.fold  seed small_stratum_size train_size_i train_size
#>                           train                  test iteration train_min_size
#>                          <list>                <list>     <int>          <int>
#>  1: 216,197, 81,171,143, 36,...  1, 7,11,13,15,19,...         1             10
#>  2: 216,197, 81,171,143, 36,...  1, 7,11,13,15,19,...         2             18
#>  3: 216,197, 81,171,143, 36,...  1, 7,11,13,15,19,...         3             33
#>  4: 216,197, 81,171,143, 36,...  1, 7,11,13,15,19,...         4             60
#>  5: 216,197, 81,171,143, 36,...  1, 7,11,13,15,19,...         5            110
#>  6: 216,197, 81,171,143, 36,...  1, 7,11,13,15,19,...         6            200
#>  7: 260,291, 16,164,109, 45,...  1, 7,11,13,15,19,...         7             10
#>  8: 260,291, 16,164,109, 45,...  1, 7,11,13,15,19,...         8             18
#>  9: 260,291, 16,164,109, 45,...  1, 7,11,13,15,19,...         9             33
#> 10: 260,291, 16,164,109, 45,...  1, 7,11,13,15,19,...        10             60
#> 11: 260,291, 16,164,109, 45,...  1, 7,11,13,15,19,...        11            110
#> 12: 260,291, 16,164,109, 45,...  1, 7,11,13,15,19,...        12            200
#> 13:  14,253,115,102,293, 18,...  1, 7,11,13,15,19,...        13             10
#> 14:  14,253,115,102,293, 18,...  1, 7,11,13,15,19,...        14             18
#> 15:  14,253,115,102,293, 18,...  1, 7,11,13,15,19,...        15             33
#> 16:  14,253,115,102,293, 18,...  1, 7,11,13,15,19,...        16             60
#> 17:  14,253,115,102,293, 18,...  1, 7,11,13,15,19,...        17            110
#> 18:  14,253,115,102,293, 18,...  1, 7,11,13,15,19,...        18            200
#> 19: 203,197, 81,171,130, 43,...  4, 6, 9,12,14,16,...        19             10
#> 20: 203,197, 81,171,130, 43,...  4, 6, 9,12,14,16,...        20             18
#> 21: 203,197, 81,171,130, 43,...  4, 6, 9,12,14,16,...        21             33
#> 22: 203,197, 81,171,130, 43,...  4, 6, 9,12,14,16,...        22             60
#> 23: 203,197, 81,171,130, 43,...  4, 6, 9,12,14,16,...        23            110
#> 24: 203,197, 81,171,130, 43,...  4, 6, 9,12,14,16,...        24            200
#> 25: 251,291, 19,164,109, 55,...  4, 6, 9,12,14,16,...        25             10
#> 26: 251,291, 19,164,109, 55,...  4, 6, 9,12,14,16,...        26             18
#> 27: 251,291, 19,164,109, 55,...  4, 6, 9,12,14,16,...        27             33
#> 28: 251,291, 19,164,109, 55,...  4, 6, 9,12,14,16,...        28             60
#> 29: 251,291, 19,164,109, 55,...  4, 6, 9,12,14,16,...        29            110
#> 30: 251,291, 19,164,109, 55,...  4, 6, 9,12,14,16,...        30            200
#> 31:  15,253,115,110,293, 18,...  4, 6, 9,12,14,16,...        31             10
#> 32:  15,253,115,110,293, 18,...  4, 6, 9,12,14,16,...        32             18
#> 33:  15,253,115,110,293, 18,...  4, 6, 9,12,14,16,...        33             33
#> 34:  15,253,115,110,293, 18,...  4, 6, 9,12,14,16,...        34             60
#> 35:  15,253,115,110,293, 18,...  4, 6, 9,12,14,16,...        35            110
#> 36:  15,253,115,110,293, 18,...  4, 6, 9,12,14,16,...        36            200
#> 37: 203,211, 82,194,130, 43,...  2, 3, 5, 8,10,17,...        37             10
#> 38: 203,211, 82,194,130, 43,...  2, 3, 5, 8,10,17,...        38             18
#> 39: 203,211, 82,194,130, 43,...  2, 3, 5, 8,10,17,...        39             33
#> 40: 203,211, 82,194,130, 43,...  2, 3, 5, 8,10,17,...        40             60
#> 41: 203,211, 82,194,130, 43,...  2, 3, 5, 8,10,17,...        41            110
#> 42: 203,211, 82,194,130, 43,...  2, 3, 5, 8,10,17,...        42            200
#> 43: 251,295, 19,189,102, 55,...  2, 3, 5, 8,10,17,...        43             10
#> 44: 251,295, 19,189,102, 55,...  2, 3, 5, 8,10,17,...        44             18
#> 45: 251,295, 19,189,102, 55,...  2, 3, 5, 8,10,17,...        45             33
#> 46: 251,295, 19,189,102, 55,...  2, 3, 5, 8,10,17,...        46             60
#> 47: 251,295, 19,189,102, 55,...  2, 3, 5, 8,10,17,...        47            110
#> 48: 251,295, 19,189,102, 55,...  2, 3, 5, 8,10,17,...        48            200
#> 49:  15,263,135,110,296, 25,...  2, 3, 5, 8,10,17,...        49             10
#> 50:  15,263,135,110,296, 25,...  2, 3, 5, 8,10,17,...        50             18
#> 51:  15,263,135,110,296, 25,...  2, 3, 5, 8,10,17,...        51             33
#> 52:  15,263,135,110,296, 25,...  2, 3, 5, 8,10,17,...        52             60
#> 53:  15,263,135,110,296, 25,...  2, 3, 5, 8,10,17,...        53            110
#> 54:  15,263,135,110,296, 25,...  2, 3, 5, 8,10,17,...        54            200
#>                           train                  test iteration train_min_size
#>
#> \$id.dt
#>      row_id  fold
#>       <int> <int>
#>   1:      1     1
#>   2:      2     3
#>   3:      3     3
#>   4:      4     2
#>   5:      5     3
#>  ---
#> 296:    296     2
#> 297:    297     1
#> 298:    298     1
#> 299:    299     3
#> 300:    300     2
``````

Above we see the instance, which need not be examined by the user, but for informational purposes, it contains the following data:

• `iteration.dt` has one row for each train/test split,
• `id.dt` has one row for each data point.

### Benchmark: computing test error

In the code below, we define two learners to compare,

``````(reg.learner.list <- list(
if(requireNamespace("rpart"))mlr3::LearnerRegrRpart\$new(),
mlr3::LearnerRegrFeatureless\$new()))
#> [[1]]
#> <LearnerRegrRpart:regr.rpart>: Regression Tree
#> * Model: -
#> * Parameters: xval=0
#> * Packages: mlr3, rpart
#> * Predict Types:  [response]
#> * Feature Types: logical, integer, numeric, factor, ordered
#> * Properties: importance, missings, selected_features, weights
#>
#> [[2]]
#> <LearnerRegrFeatureless:regr.featureless>: Featureless Regression Learner
#> * Model: -
#> * Parameters: robust=FALSE
#> * Packages: mlr3, stats
#> * Predict Types:  [response], se
#> * Feature Types: logical, integer, numeric, character, factor, ordered,
#>   POSIXct
#> * Properties: featureless, importance, missings, selected_features
``````

The code above defines

• `regr.rpart`: Regression Tree learning algorithm, which should be able to learn the non-linear pattern in the sin data (if there are enough data in the train set).
• `regr.featureless`: Featureless Regression learning algorithm, which should be optimal for the constant data, and can be used as a baseline in the sin data. When the rpart learner gets smaller prediction error rates than featureless, then we know that it has learned some non-trivial relationship between inputs and outputs.

In the code below, we define the benchmark grid, which is all combinations of tasks (constant and sin), learners (rpart and featureless), and the one resampling method.

``````(reg.bench.grid <- mlr3::benchmark_grid(
reg.learner.list,
reg_size_cv))
#>      <char>           <char>                 <char>
#> 1:      sin       regr.rpart variable_size_train_cv
#> 2:      sin regr.featureless variable_size_train_cv
#> 3: constant       regr.rpart variable_size_train_cv
#> 4: constant regr.featureless variable_size_train_cv
``````

In the code below, we execute the benchmark experiment (optionally in parallel using the multisession future plan).

``````if(FALSE){
if(require(future))plan("multisession")
}
if(require(lgr))get_logger("mlr3")\$set_threshold("warn")
(reg.bench.result <- mlr3::benchmark(
reg.bench.grid, store_models = TRUE))
#> <BenchmarkResult> of 216 rows with 4 resampling runs
#>  nr  task_id       learner_id          resampling_id iters warnings errors
#>   1      sin       regr.rpart variable_size_train_cv    54        0      0
#>   2      sin regr.featureless variable_size_train_cv    54        0      0
#>   3 constant       regr.rpart variable_size_train_cv    54        0      0
#>   4 constant regr.featureless variable_size_train_cv    54        0      0
``````

The code below computes the test error for each split, and visualizes the information stored in the first row of the result:

``````reg.bench.score <- mlr3resampling::score(reg.bench.result)
reg.bench.score[1]
#>    test.fold  seed small_stratum_size train_size_i train_size
#>        <int> <int>              <int>        <int>      <int>
#> 1:         1     1                 10            1         10
#>                          train                  test iteration train_min_size
#>                         <list>                <list>     <int>          <int>
#> 1: 216,197, 81,171,143, 36,...  1, 7,11,13,15,19,...         1             10
#>                                  <char> <int>         <list>  <char>
#> 1: 50d4edb9-631c-4ece-b745-efbdeba0e44c     1 <TaskRegr:sin>     sin
#>                          learner learner_id                      resampling
#>                           <list>     <char>                          <list>
#> 1: <LearnerRegrRpart:regr.rpart> regr.rpart <ResamplingVariableSizeTrainCV>
#>             resampling_id       prediction  regr.mse algorithm
#>                    <char>           <list>     <num>    <char>
#> 1: variable_size_train_cv <PredictionRegr> 0.8008255     rpart
``````

The output above contains all of the results related to a particular train/test split. In particular for our purposes, the interesting columns are:

• `test.fold` is the cross-validation fold ID.
• `seed` is the random seed used to determine the train set order.
• `train_size` is the number of data in the train set.
• `train` and `test` are vectors of row numbers assigned to each set.
• `iteration` is an ID for the train/test split, for a particular learning algorithm and task. It is the row number of `iteration.dt` (see instance above), which has one row for each unique combination of `test.fold`, `seed`, and `train_size`.
• `learner` is the mlr3 learner object, which can be used to compute predictions on new data (including a grid of inputs, to show predictions in the visualization below).
• `regr.mse` is the mean squared error on the test set.
• `algorithm` is the name of the learning algorithm (same as `learner_id` but without `regr.` prefix).

The code below visualizes the resulting test accuracy numbers.

``````train_size_vec <- unique(reg.bench.score\$train_size)
if(require(animint2)){
ggplot()+
scale_x_log10(
breaks=train_size_vec)+
scale_y_log10()+
geom_line(aes(
train_size, regr.mse,
group=paste(algorithm, seed),
color=algorithm),
shape=1,
data=reg.bench.score)+
geom_point(aes(
train_size, regr.mse, color=algorithm),
shape=1,
data=reg.bench.score)+
facet_grid(
labeller=label_both,
scales="free")
}
``````

Above we plot the test error for each fold and train set size. There is a different panel for each task and test fold. Each line represents a random seed (ordering of data in train set), and each dot represents a specific train set size. So the plot above shows that some variation in test error, for a given test fold, is due to the random ordering of the train data.

Below we summarize each train set size, by taking the mean and standard deviation over each random seed.

``````reg.mean.dt <- dcast(
reg.bench.score,
task_id + train_size + test.fold + algorithm ~ .,
list(mean, sd),
value.var="regr.mse")
if(require(animint2)){
ggplot()+
scale_x_log10(
breaks=train_size_vec)+
scale_y_log10()+
geom_ribbon(aes(
train_size,
ymin=regr.mse_mean-regr.mse_sd,
ymax=regr.mse_mean+regr.mse_sd,
fill=algorithm),
alpha=0.5,
data=reg.mean.dt)+
geom_line(aes(
train_size, regr.mse_mean, color=algorithm),
shape=1,
data=reg.mean.dt)+
facet_grid(
labeller=label_both,
scales="free")
}
``````

The plot above shows a line for the mean, and a ribbon for the standard deviation, over the three random seeds. It is clear from the plot above that

• in constant task, the featureless always has smaller or equal prediction error rates than rpart, which indicates that rpart sometimes overfits for large sample sizes.
• in sin task, more than 30 samples are required for rpart to be more accurate than featureless, which indicates it has learned a non-trivial relationship between input and output.

### Interactive data viz

The code below can be used to create an interactive data visualization which allows exploring how different functions are learned during different splits.

``````grid.dt <- data.table(x=seq(-abs.x, abs.x, l=101), y=0)
pred.dt.list <- list()
point.dt.list <- list()
for(score.i in 1:nrow(reg.bench.score)){
reg.bench.row <- reg.bench.score[score.i]
reg.bench.row\$resampling[[1]]\$instance\$id.dt)
set.ids <- data.table(
set.name=c("test","train")
)[
, data.table(row_id=reg.bench.row[[set.name]][[1]])
, by=set.name]
i.points <- set.ids[
][
is.na(set.name), set.name := "unused"
]
point.dt.list[[score.i]] <- data.table(
i.points)
i.learner <- reg.bench.row\$learner[[1]]
pred.dt.list[[score.i]] <- data.table(
reg.bench.row[, .(
)],
as.data.table(
)[, .(x=grid.dt\$x, y=response)]
)
}
(pred.dt <- rbindlist(pred.dt.list))
#>         task_id iteration   algorithm     x           y
#>          <char>     <int>      <char> <num>       <num>
#>     1:      sin         1       rpart -10.0  0.25011658
#>     2:      sin         1       rpart  -9.8  0.25011658
#>     3:      sin         1       rpart  -9.6  0.25011658
#>     4:      sin         1       rpart  -9.4  0.25011658
#>     5:      sin         1       rpart  -9.2  0.25011658
#>    ---
#> 21812: constant        54 featureless   9.2 -0.03385654
#> 21813: constant        54 featureless   9.4 -0.03385654
#> 21814: constant        54 featureless   9.6 -0.03385654
#> 21815: constant        54 featureless   9.8 -0.03385654
#> 21816: constant        54 featureless  10.0 -0.03385654
(point.dt <- rbindlist(point.dt.list))
#>         task_id iteration set.name row_id          y         x  fold
#>          <char>     <int>   <char>  <int>      <num>     <num> <int>
#>     1:      sin         1     test      1  1.2248390 -4.689827     1
#>     2:      sin         1   unused      2 -0.5607042 -2.557522     3
#>     3:      sin         1   unused      3  0.8345056  1.457067     3
#>     4:      sin         1   unused      4  0.4875994  8.164156     2
#>     5:      sin         1   unused      5 -0.4321800 -5.966361     3
#>    ---
#> 64796: constant        54    train    296 -0.6728968  3.628850     2
#> 64797: constant        54    train    297  0.5168327 -8.016618     1
#> 64798: constant        54    train    298 -0.4058882 -7.621949     1
#> 64799: constant        54     test    299  0.9008627 -8.991207     3
#> 64800: constant        54    train    300  0.8857710  8.585078     2
set.colors <- c(
train="#1B9E77",
test="#D95F02",
unused="white")
algo.colors <- c(
featureless="blue",
rpart="red")
if(require(animint2)){
viz <- animint(
title="Variable size train set, regression",
pred=ggplot()+
ggtitle("Predictions for selected train/test split")+
theme_animint(height=400)+
scale_fill_manual(values=set.colors)+
geom_point(aes(
x, y, fill=set.name),
showSelected="iteration",
size=3,
shape=21,
data=point.dt)+
scale_size_manual(values=c(
featureless=3,
rpart=2))+
scale_color_manual(values=algo.colors)+
geom_line(aes(
x, y,
color=algorithm,
size=algorithm,
group=paste(algorithm, iteration)),
showSelected="iteration",
data=pred.dt)+
facet_grid(
labeller=label_both),
err=ggplot()+
ggtitle("Test error for each split")+
theme_animint(width=500)+
theme(
panel.margin=grid::unit(1, "lines"),
legend.position="none")+
scale_y_log10(
"Mean squared error on test set")+
scale_color_manual(values=algo.colors)+
scale_x_log10(
"Train set size",
breaks=train_size_vec)+
geom_line(aes(
train_size, regr.mse,
group=paste(algorithm, seed),
color=algorithm),
clickSelects="seed",
alpha_off=0.2,
showSelected="algorithm",
size=4,
data=reg.bench.score)+
facet_grid(
labeller=label_both,
scales="free")+
geom_point(aes(
train_size, regr.mse,
color=algorithm),
size=5,
stroke=3,
fill="black",
fill_off=NA,
showSelected=c("algorithm","seed"),
clickSelects="iteration",
data=reg.bench.score),
source="https://github.com/tdhock/mlr3resampling/blob/main/vignettes/Simulations.Rmd")
viz
}
``````

``````if(FALSE){
animint2pages(viz, "2023-12-26-train-sizes-regression")
}
``````

If you are viewing this in an installed package or on CRAN, then there will be no data viz on this page, but you can view it on: https://tdhock.github.io/2023-12-26-train-sizes-regression/

The interactive data viz consists of two plots:

• The first plot shows the data, with each point colored according to the set it was assigned, in the currently selected split/iteration. The red/blue lines additionally show the learned prediction functions for the currently selected split/iteration.
• The second plot shows the test error rates, as a function of train set size. Clicking a line selects the corresponding random seed, which makes the corresponding points on that line appear. Clicking a point selects the corresponding iteration (seed, test fold, and train set size).

## Simulated classification problems

Whereas in the section above, we focused on regression (output is a real number), in this section we simulate a binary classification problem (output if a factor with two levels).

``````class.N <- 300
class.abs.x <- 1
rclass <- function(){
runif(class.N, -class.abs.x, class.abs.x)
}
library(data.table)
set.seed(1)
class.x.dt <- data.table(x1=rclass(), x2=rclass())
class.fun.list <- list(
constant=function(...)0.5,
xor=function(x1, x2)xor(x1>0, x2>0))
class.data.list <- list()
y <- factor(ifelse(
class.x.dt[, class.fun(x1, x2)+rnorm(class.N, sd=0.5)]>0.5,
"spam", "not"))
}
(class.data <- rbindlist(class.data.list))
#>        <char>      <num>        <num> <fctr>
#>   1: constant -0.4689827  0.347424466   spam
#>   2: constant -0.2557522 -0.810284289    not
#>   3: constant  0.1457067 -0.014807758   spam
#>   4: constant  0.8164156 -0.076896319    not
#>   5: constant -0.5966361 -0.249566938   spam
#>  ---
#> 596:      xor  0.3628850  0.297101895    not
#> 597:      xor -0.8016618 -0.040328411    not
#> 598:      xor -0.7621949 -0.009871789   spam
#> 599:      xor -0.8991207 -0.240254817    not
#> 600:      xor  0.8585078 -0.099029126   spam
``````

The simulated data table above consists of two input features (`x1` and `x2`) along with an output/label to predict (`y`). Below we count the number of times each label appears in each task:

``````class.data[, .(count=.N), by=.(task_id, y)]
#>      <char> <fctr> <int>
#> 1: constant   spam   143
#> 2: constant    not   157
#> 3:      xor   spam   145
#> 4:      xor    not   155
``````

The table above shows that the `spam` label is the minority class (`not` is majority, so that will be the prediction of the featureless baseline). Below we visualize the data in the feature space:

``````if(require(animint2)){
ggplot()+
geom_point(aes(
x1, x2, color=y),
shape=1,
data=class.data)+
coord_equal()
}
``````

The plot above shows how the output `y` is related to the two inputs `x1` and `x2`, for the two tasks.

• For the constant task, the two inputs are not related to the output.
• For the xor task, the spam label is associated with either `x1` or `x2` being negative (but not both).

In the mlr3 code below, we define a list of learners, our resampling method, and a benchmark grid:

``````class.learner.list <- list(
if(requireNamespace("rpart"))mlr3::LearnerClassifRpart\$new(),
mlr3::LearnerClassifFeatureless\$new())
size_cv <- mlr3resampling::ResamplingVariableSizeTrainCV\$new()
(class.bench.grid <- mlr3::benchmark_grid(
class.learner.list,
size_cv))
#>      <char>              <char>                 <char>
#> 1: constant       classif.rpart variable_size_train_cv
#> 2: constant classif.featureless variable_size_train_cv
#> 3:      xor       classif.rpart variable_size_train_cv
#> 4:      xor classif.featureless variable_size_train_cv
``````

Below we run the learning algorithm for each of the train/test splits defined by our benchmark grid:

``````if(FALSE){
if(require(future))plan("multisession")
}
if(require(lgr))get_logger("mlr3")\$set_threshold("warn")
(class.bench.result <- mlr3::benchmark(
class.bench.grid, store_models = TRUE))
#> <BenchmarkResult> of 180 rows with 4 resampling runs
#>  nr  task_id          learner_id          resampling_id iters warnings errors
#>   1 constant       classif.rpart variable_size_train_cv    45        0      0
#>   2 constant classif.featureless variable_size_train_cv    45        0      0
#>   3      xor       classif.rpart variable_size_train_cv    45        0      0
#>   4      xor classif.featureless variable_size_train_cv    45        0      0
``````

Below we compute scores (test error) for each resampling iteration, and show the first row of the result.

``````class.bench.score <- mlr3resampling::score(class.bench.result)
class.bench.score[1]
#>    test.fold  seed small_stratum_size train_size_i train_size
#>        <int> <int>              <int>        <int>      <int>
#> 1:         1     1                 10            1         21
#>                          train                  test iteration train_min_size
#>                         <list>                <list>     <int>          <int>
#> 1: 132,239, 10,216,245,276,...  5, 6, 8,21,23,28,...         1             21
#>                                  <char> <int>                 <list>   <char>
#> 1: e960895e-2364-4ec6-8f99-48c776d2273f     1 <TaskClassif:constant> constant
#>                                learner    learner_id
#>                                 <list>        <char>
#> 1: <LearnerClassifRpart:classif.rpart> classif.rpart
#>                         resampling          resampling_id          prediction
#>                             <list>                 <char>              <list>
#> 1: <ResamplingVariableSizeTrainCV> variable_size_train_cv <PredictionClassif>
#>    classif.ce algorithm
#>         <num>    <char>
#> 1:  0.4257426     rpart
``````

The output above has columns which are very similar to the regression example in the previous section. The main difference is the `classif.ce` column, which is the classification error on the test set.

Finally we plot the test error values below.

``````if(require(animint2)){
ggplot()+
geom_line(aes(
train_size, classif.ce,
group=paste(algorithm, seed),
color=algorithm),
shape=1,
data=class.bench.score)+
geom_point(aes(
train_size, classif.ce, color=algorithm),
shape=1,
data=class.bench.score)+
facet_grid(
labeller=label_both,
scales="free")+
scale_x_log10()
}
``````

It is clear from the plot above that

• in constant task, rpart does not have significantly lower error rates than featureless, which is expected, because the best prediction function is constant (predict the most frequent class, no relationship between inputs and output).
• in xor task, more than 30 samples are required for rpart to be more accurate than featureless, which indicates it has learned a non-trivial relationship between inputs and output.

Exercise for the reader: compute and plot mean and SD for these classification tasks, similar to the plot for the regression tasks in the previous section.

### Interactive visualization of data, test error, and splits

The code below can be used to create an interactive data visualization which allows exploring how different functions are learned during different splits.

``````class.grid.vec <- seq(-class.abs.x, class.abs.x, l=21)
class.grid.dt <- CJ(x1=class.grid.vec, x2=class.grid.vec)
class.pred.dt.list <- list()
class.point.dt.list <- list()
for(score.i in 1:nrow(class.bench.score)){
class.bench.row <- class.bench.score[score.i]
class.bench.row\$resampling[[1]]\$instance\$id.dt)
set.ids <- data.table(
set.name=c("test","train")
)[
, data.table(row_id=class.bench.row[[set.name]][[1]])
, by=set.name]
i.points <- set.ids[
][
is.na(set.name), set.name := "unused"
][]
class.point.dt.list[[score.i]] <- data.table(
i.points)
if(class.bench.row\$algorithm!="featureless"){
i.learner <- class.bench.row\$learner[[1]]
i.learner\$predict_type <- "prob"
pred.grid <- as.data.table(
)[, data.table(class.grid.dt, prob.spam)]
pred.wide <- dcast(pred.grid, x1 ~ x2, value.var="prob.spam")
prob.mat <- as.matrix(pred.wide[,-1])
if(length(table(prob.mat))>1){
contour.list <- contourLines(
class.grid.vec, class.grid.vec, prob.mat, levels=0.5)
class.pred.dt.list[[score.i]] <- data.table(
class.bench.row[, .(
)],
data.table(contour.i=seq_along(contour.list))[, {
do.call(data.table, contour.list[[contour.i]])[, .(level, x1=x, x2=y)]
}, by=contour.i]
)
}
}
}
(class.pred.dt <- rbindlist(class.pred.dt.list))
#>        task_id iteration algorithm contour.i level     x1          x2
#>         <char>     <int>    <char>     <int> <num>  <num>       <num>
#>    1: constant         1     rpart         1   0.5 0.0375 -1.00000000
#>    2: constant         1     rpart         1   0.5 0.0375 -0.90000000
#>    3: constant         1     rpart         1   0.5 0.0375 -0.80000000
#>    4: constant         1     rpart         1   0.5 0.0375 -0.70000000
#>    5: constant         1     rpart         1   0.5 0.0375 -0.60000000
#>   ---
#> 5190:      xor        45     rpart         2   0.5 0.6000  0.04888889
#> 5191:      xor        45     rpart         2   0.5 0.7000  0.04888889
#> 5192:      xor        45     rpart         2   0.5 0.8000  0.04888889
#> 5193:      xor        45     rpart         2   0.5 0.9000  0.04888889
#> 5194:      xor        45     rpart         2   0.5 1.0000  0.04888889
(class.point.dt <- rbindlist(class.point.dt.list))
#>         task_id iteration set.name row_id      y         x1           x2  fold
#>          <char>     <int>   <char>  <int> <fctr>      <num>        <num> <int>
#>     1: constant         1   unused      1   spam -0.4689827  0.347424466     3
#>     2: constant         1   unused      2    not -0.2557522 -0.810284289     2
#>     3: constant         1   unused      3   spam  0.1457067 -0.014807758     3
#>     4: constant         1    train      4    not  0.8164156 -0.076896319     3
#>     5: constant         1     test      5   spam -0.5966361 -0.249566938     1
#>    ---
#> 53996:      xor        45    train    296    not  0.3628850  0.297101895     2
#> 53997:      xor        45    train    297    not -0.8016618 -0.040328411     2
#> 53998:      xor        45     test    298   spam -0.7621949 -0.009871789     3
#> 53999:      xor        45     test    299    not -0.8991207 -0.240254817     3
#> 54000:      xor        45    train    300   spam  0.8585078 -0.099029126     2

set.colors <- c(
train="#1B9E77",
test="#D95F02",
unused="white")
algo.colors <- c(
featureless="blue",
rpart="red")
if(require(animint2)){
viz <- animint(
title="Variable size train sets, classification",
pred=ggplot()+
ggtitle("Predictions for selected train/test split")+
theme(panel.margin=grid::unit(1, "lines"))+
theme_animint(width=600)+
coord_equal()+
scale_fill_manual(values=set.colors)+
scale_color_manual(values=c(spam="black","not spam"="white"))+
geom_point(aes(
x1, x2, color=y, fill=set.name),
showSelected="iteration",
size=3,
stroke=2,
shape=21,
data=class.point.dt)+
geom_path(aes(
x1, x2,
group=paste(algorithm, iteration, contour.i)),
showSelected=c("iteration","algorithm"),
color=algo.colors[["rpart"]],
data=class.pred.dt)+
facet_grid(
labeller=label_both,
space="free",
scales="free"),
err=ggplot()+
ggtitle("Test error for each split")+
theme_animint(height=400)+
theme(panel.margin=grid::unit(1, "lines"))+
scale_y_continuous(
"Classification error on test set")+
scale_color_manual(values=algo.colors)+
scale_x_log10(
"Train set size")+
geom_line(aes(
train_size, classif.ce,
group=paste(algorithm, seed),
color=algorithm),
clickSelects="seed",
alpha_off=0.2,
showSelected="algorithm",
size=4,
data=class.bench.score)+
facet_grid(
labeller=label_both,
scales="free")+
geom_point(aes(
train_size, classif.ce,
color=algorithm),
size=5,
stroke=3,
fill="black",
fill_off=NA,
showSelected=c("algorithm","seed"),
clickSelects="iteration",
data=class.bench.score),
source="https://github.com/tdhock/mlr3resampling/blob/main/vignettes/ResamplingVariableSizeTrainCV.Rmd")
viz
}
``````

``````if(FALSE){
animint2pages(viz, "2023-12-27-train-sizes-classification")
}
``````

If you are viewing this in an installed package or on CRAN, then there will be no data viz on this page, but you can view it on: https://tdhock.github.io/2023-12-27-train-sizes-classification/

The interactive data viz consists of two plots

• The first plot shows the data, with each point colored according to its label/y value (black outline for spam, white outline for not), and the set it was assigned (fill color) in the currently selected split/iteration. The red lines additionally show the learned decision boundary for rpart, given the currently selected split/iteration. For constant, the ideal decision boundary is none (always predict the most frequent class), and for xor, the ideal decision boundary looks like a plus sign.
• The second plot shows the test error rates, as a function of train set size. Clicking a line selects the corresponding random seed, which makes the corresponding points on that line appear. Clicking a point selects the corresponding iteration (seed, test fold, and train set size).

## Conclusion

In this section we have shown how to use mlr3resampling for comparing test error of models trained on different sized train sets.

# Session info

``````sessionInfo()
#> R version 4.3.2 (2023-10-31)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 18.04.6 LTS
#>
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
#> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
#>
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
#>  [3] LC_TIME=fr_FR.UTF-8        LC_COLLATE=C
#>  [5] LC_MONETARY=fr_FR.UTF-8    LC_MESSAGES=en_US.UTF-8
#>  [7] LC_PAPER=fr_FR.UTF-8       LC_NAME=C
#> [11] LC_MEASUREMENT=fr_FR.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: America/Toronto
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base
#>
#> other attached packages:
#> [1] lgr_0.4.4              animint2_2024.3.12     directlabels_2024.1.21
#> [4] mlr3_0.17.0            ggplot2_3.5.0          data.table_1.15.0
#>
#> loaded via a namespace (and not attached):
#>  [1] utf8_1.2.4              future_1.33.0           generics_0.1.3
#>  [4] stringi_1.8.3           listenv_0.9.1           digest_0.6.34
#>  [7] magrittr_2.0.3          evaluate_0.23           grid_4.3.2
#> [10] plyr_1.8.9              backports_1.4.1         fansi_1.0.6
#> [13] mlr3resampling_2024.7.7 scales_1.3.0            mlr3tuning_0.19.2
#> [16] codetools_0.2-19        mlr3measures_0.5.0      palmerpenguins_0.1.1
#> [19] cli_3.6.2               rlang_1.1.3             crayon_1.5.2
#> [22] parallelly_1.37.0       future.apply_1.11.0     munsell_0.5.0
#> [25] commonmark_1.9.1        withr_3.0.0             nc_2024.2.21
#> [28] tools_4.3.2             parallel_4.3.2          reshape2_1.4.4
#> [31] RJSONIO_1.3-1.9         uuid_1.1-1              checkmate_2.3.1
#> [34] dplyr_1.1.4             colorspace_2.1-0        globals_0.16.2
#> [37] bbotk_0.7.3             vctrs_0.6.5             R6_2.5.1
#> [40] mime_0.12               rpart_4.1.23            lifecycle_1.0.4
#> [43] stringr_1.5.1           mlr3misc_0.13.0         pkgconfig_2.0.3
#> [46] pillar_1.9.0            gtable_0.3.4            Rcpp_1.0.12