The Split-Apply-Combine Technique for Machine Learning with R

Introduction

Much discussion in the R community has revolved around the proper way to implement the “split-apply-combine”. In particular, I love the exploration of this topic in this blog post. It seems that the “preferred” approach is dplyr::group_by() + tidyr::nest() for splitting, dplyr::mutate() + purrr::map() for applying, and tidyr::unnest() for combining.

Additionally, many in the community have shown implementations of the “many models” approach in {tidyverse}-style pipelines, often also using the {broom} package. For example, see any one of Dr. Simon J’s many blog posts on machine learning, such as this one on k-fold cross validation.

However, I haven’t seen as much exploration of how to apply the split-apply-combine technique to machine learning with the {caret} package, which is perhaps the most popular “generic” R machine learning package (along with {mlr}). One interesting write-up that I found on this subject is this one by Rahul S.. Thus, I was inspired to experiment with my own {tidyverse}-like pipelines using {caret}. (I actually used these techniques in my homework solutions to the edX Georgia Tech Introduction to Analytics Modeling class that I have been taking this summer.)

Setup

For this walk-through, I’ll be exploring the PrimaIndiansDiabetes data set provided by the {mlbench} package. This data set was originally collected by the National Institute of Diabetes and Digestive and Kidney Diseases and published as one of the many datasets available in the UCI Repository. It consists of 768 rows and 9 variables. It is useful for practicing binary classification, where the diabetes class variable (consisting of pos and neg values) is the response which I aim to predict.

data("PimaIndiansDiabetes", package = "mlbench")

PimaIndiansDiabetes

##     pregnant glucose pressure triceps insulin mass pedigree age diabetes
## 1          6     148       72      35       0   34    0.627  50      pos
## 2          1      85       66      29       0   27    0.351  31      neg
## 3          8     183       64       0       0   23    0.672  32      pos
## 4          1      89       66      23      94   28    0.167  21      neg
## 5          0     137       40      35     168   43    2.288  33      pos
## 6          5     116       74       0       0   26    0.201  30      neg
## 7          3      78       50      32      88   31    0.248  26      pos
## 8         10     115        0       0       0   35    0.134  29      neg
## 9          2     197       70      45     543   30    0.158  53      pos
## 10         8     125       96       0       0    0    0.232  54      pos
## 11         4     110       92       0       0   38    0.191  30      neg
##  [ reached getOption("max.print") -- omitted 757 rows ]

fmla_diabetes <- formula(diabetes ~ .)

Additionally, I’ll be using the {tidyverse} suite of packages—most notably {dplyr}, {purrr}, and {tidyr}—as well as the {caret} package for its machine learning API.

library("tidyverse")
library("caret")

Traditional {caret} Usage

First, I think it’s instructive to show how one might typically use {caret} to create individual models so that I can create a baseline with which to compare a “many models” approach.

So, let’s say that I want to fit a cross-validated CART (classification and regression tree) model with scaling and a grid of reasonable complexity parameter (cp) values. (I don’t show the output here because the code is shown purely for exemplary purposes.)

fit_rpart <-
  train(
    form = fmla_diabetes,
    data = PimaIndiansDiabetes,
    method = "rpart",
    preProcess = "scale",
    trControl = trainControl(method = "cv", number = 5),
    metric = "Accuracy",
    minsplit = 5,
    tuneGrid = data.frame(cp = 10 ^ seq(-2, 1, by = 1))
  )
fit_rpart

## CART 
## 
## 768 samples
##   8 predictor
##   2 classes: 'neg', 'pos' 
## 
## Pre-processing: scaled (8) 
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 615, 614, 614, 614, 615 
## Resampling results across tuning parameters:
## 
##   cp     Accuracy  Kappa
##    0.01  0.74      0.43 
##    0.10  0.73      0.36 
##    1.00  0.65      0.00 
##   10.00  0.65      0.00 
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.01.

It’s reasonable to use {caret} directly in the manner shown above when simply fitting one model. But, let’s say that now you want to compare the previous results with a model fit with un-scaled predictors (perhaps for pedagogical purposes. Now you copy-paste the previous statement, only modifying preProcess from "scale" to NULL.

fit_rpart_unscaled <-
  train(
    form = fmla_diabetes,
    data = PimaIndiansDiabetes,
    method = "rpart",
    preProcess = NULL,
    trControl = trainControl(method = "cv", number = 5),
    metric = "Accuracy",
    minsplit = 5,
    tuneGrid = data.frame(cp = 10 ^ seq(-2, 1, by = 1))
  )
fit_rpart_unscaled

## CART 
## 
## 768 samples
##   8 predictor
##   2 classes: 'neg', 'pos' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 614, 615, 614, 614, 615 
## Resampling results across tuning parameters:
## 
##   cp     Accuracy  Kappa
##    0.01  0.73      0.40 
##    0.10  0.72      0.36 
##    1.00  0.65      0.00 
##   10.00  0.65      0.00 
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.01.

Although I might feel bad about copying-and-pasting so much code, I end up with what I wanted.

But now I want to try a different method–a random forest. Now I will need to change the value of the method argument (to "rf") and the value of tuneGrid—because there are different parameters to tune for a random forest—and remove the minsplit argument—because it is not applicable for the caret::train() method for "rf", and, consequently, will cause an error.

fit_rf <-
  train(
    form = fmla_diabetes,
    data = PimaIndiansDiabetes,
    method = "rf",
    preProcess = "scale",
    trControl = trainControl(method = "cv", number = 5),
    metric = "Accuracy",
    tuneGrid = data.frame(mtry = c(3, 5, 7))
  )
fit_rf

## Random Forest 
## 
## 768 samples
##   8 predictor
##   2 classes: 'neg', 'pos' 
## 
## Pre-processing: scaled (8) 
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 614, 614, 614, 615, 615 
## Resampling results across tuning parameters:
## 
##   mtry  Accuracy  Kappa
##   3     0.76      0.46 
##   5     0.75      0.44 
##   7     0.75      0.44 
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 3.

Then, what if I want to try yet another different method (with the same formula (form) and data)? I would have to continue copy-pasting like this, which, of course, can start to become tiresome. The DRY principle is certainly relevant here—an approach using functions to automate the re-implementation the “constants” among methods is superior.

Anyways, I think it is evident that a better approach than copy-pasting code endlessly can be achieved. With that said, next I’ll demonstrate two approaches. While I believe the second of these is superior because it is less verbose, I think it’s worth showing the first approach as well for instructive purposes.

split-apply-combine + {caret}, Approach #1

For this first approach,

1. First, I define a “base” function that creates a list of arguments passed to caret::train() that are common among each of the methods to evaluate.
2. Next, I define several “method-specific” functions for rpart", "rf", and "ranger" (a faster implementation of the random forest than that of the more well known {randomForest} package, which is used by the "rf" method for caret::train()). These functions return lists of parameters for caret::train() that are unique for each function—most notably tuneGrid. (The {caret} package’s documentation should be consulted to identify exactly which arguments must be defined.) Additionally, note that there may be parameters that are passed directly to the underlying function called by caret::train() (via the ... argument). such as minsplit for the "rpart". (
3. Finally, I define a sprintf-style function—with method as an argument—to call the method-specific functions (using purrr::invoke()).

Thus, the call stack for this approach looks like this. ¹

setup_caret_base_tree <-
  function() {
    list(
      form = fmla_diabetes,
      data = PimaIndiansDiabetes,
      trControl = trainControl(method = "cv", number = 5),
      metric = "Accuracy"
    )
  }

setup_caret_rpart <-
  function() {
    list(method = "rpart",
         minsplit = 5,
         tuneGrid = data.frame(cp = 10 ^ seq(-2, 1, by = 1)))
  }

setup_caret_rf <-
  function() {
   list(method = "rf", tuneGrid = data.frame(mtry = c(3, 5, 7)))
  }

setup_caret_ranger <-
  function() {
    list(method = "ranger",
         tuneGrid = 
           expand.grid(
             mtry = c(3, 5, 7),
             splitrule = c("gini"),
             min.node.size = 5,
             stringsAsFactors = FALSE
            )
    )
  }

fit_caret_tree_sprintf <-
  function(method, preproc = NULL) {
    invoke(
      train,
      c(
        invoke(setup_caret_base_tree),
        invoke(sprintf("setup_caret_%s", method)),
        preProcess = preproc
      )
    )
  }

(I apologize if the _tree suffix with the functions defined here seems verbose, but I think this syntax servers as an informational “hint” that other functions with non-tree-based methods could be written in a similar fashion.)

Next, I define the “grids” of method and pre-processing specifications to pass to the functions. I define a relatively “minimal” set of different combinations in order to emphasize the functionality that is implemented (rather than the choices for methods and pre-processing).

Note the following:

• The _desc column(s) are purely for informative purposes—they aren’t used in the functions.
• The idx_method column is defined for use as the key column in the join that it does to combine these “grid” specifications and the functions when the functions are called. (See fits_diabetes_tree.)
• I want to try methods without any pre-processing, meaning that preProcess should be set to NULL in caret::train(). However, it is not possible (to my knowledge) to explicitly define a NULL in a data.frame, so I use the surrogate "none", which gets ignored (i.e. treated as NULL) when passed as the value of preProcess to caret::train().
• The method and preproc columns are not actually used directly for this approach, but for the next one.

grid_preproc <-
  tribble(
    ~preprocess_desc, ~preproc,
    "Scaled", "scale",
    "Unscaled", "none"
  )

grid_methods_tree <-
  tribble(
    ~method_desc, ~method,
    "{rpart} CART", "rpart",
    "{randomForest} Random Forest", "rf",
    "{ranger} Random Forest", "ranger"
  ) %>% 
  crossing(
    grid_preproc
  ) %>% 
  unite(method_desc, method_desc, preprocess_desc, sep = ", ") %>% 
  mutate(idx_method = row_number()) %>% 
  select(idx_method, everything())
grid_methods_tree

## # A tibble: 6 x 4
##   idx_method method_desc                            method preproc
##        <int> <chr>                                  <chr>  <chr>  
## 1          1 {rpart} CART, Scaled                   rpart  scale  
## 2          2 {rpart} CART, Unscaled                 rpart  none   
## 3          3 {randomForest} Random Forest, Scaled   rf     scale  
## 4          4 {randomForest} Random Forest, Unscaled rf     none   
## 5          5 {ranger} Random Forest, Scaled         ranger scale  
## 6          6 {ranger} Random Forest, Unscaled       ranger none

Finally, for the actual implementation, I call fit_caret_tree_sprintf() for each combination of method and pre-processing transformation(s). Importantly, the calls should be made in the same order as that implied by grid_methods_tree so that the join on idx_method is “valid” (in the sense that the model fit aligns with the description).

set.seed(42)
fits_diabetes_tree_1 <-
  tribble(
    ~fit,
    fit_caret_tree_sprintf(method = "rpart", preproc = NULL),
    fit_caret_tree_sprintf(method = "rpart", preproc = "scale"),
    fit_caret_tree_sprintf(method = "rf", preproc = NULL),
    fit_caret_tree_sprintf(method = "rf", preproc = "scale"),
    fit_caret_tree_sprintf(method = "ranger", preproc = NULL),
    fit_caret_tree_sprintf(method = "ranger", preproc = "scale")
  ) %>% 
  mutate(idx_method = row_number()) %>% 
  left_join(grid_methods_tree) %>% 
  # Rearranging so that `fit` is the last column.
  select(-fit, everything(), fit)
fits_diabetes_tree_1

## # A tibble: 6 x 5
##   idx_method method_desc                         method preproc fit       
##        <int> <chr>                               <chr>  <chr>   <list>    
## 1          1 {rpart} CART, Scaled                rpart  scale   <S3: trai~
## 2          2 {rpart} CART, Unscaled              rpart  none    <S3: trai~
## 3          3 {randomForest} Random Forest, Scal~ rf     scale   <S3: trai~
## 4          4 {randomForest} Random Forest, Unsc~ rf     none    <S3: trai~
## 5          5 {ranger} Random Forest, Scaled      ranger scale   <S3: trai~
## 6          6 {ranger} Random Forest, Unscaled    ranger none    <S3: trai~

I get the results that I wanted, albeit with a bit more verbosity than I might have liked. (Note the repeated calls to the sprintf function.)

There are a couple of other things that I did not mention before about the code that I think are worth saying.

• If one does not wish to specify tuneGrid, then the implementation becomes simpler.
• Other purrr functions such as partial() or compose() could possibly be used in some manner to reduce some of the redundant code to an even greater extent.
• If one only wants to implement pre-processing for certain methods, then the method-specific functions and the sprintf function could be re-defined such that preproc is passed as an argument to the method-specific functions and not used in the sprintf function.

split-apply-combine + {caret}, Approach #2

For this next approach (my preferred one), the fundamental difference is with the use of the grid_methods_tree data.frame created before. Because the split-apply-combine recipe for this approach directly uses the method and preproc columns—recall that these are not used with the previous approach—it is necessary to use grid_methods_tree at the beginning of the modeling pipeline.

Because I use the grid_methods_tree columns directly, I remove much of the verbosity seen in the prior approach. Now I define a function that essentially serves the same purpose as the sprintf function defined before—it binds the lists returned by a base {caret} function and a method-specific {caret} function, as well as a value for the preProcess argument.

There is a bit of “hacky” part of the implementation here—I use a switch() statement in order to substitute NULL for "none". As mentioned before, it does not seem possible to create a NULL value in a data.frame, so "none" serves as a “stand-in”. Notably, an ifelse() call does not work because it cannot return a NULL.

fit_caret_tree <-
  function(method, preproc = "scale") {
    invoke(
      train,
      c(
        invoke(setup_caret_base_tree),
        invoke(sprintf("setup_caret_%s", method)),
        preProcess = switch(preproc == "none", NULL, preproc)
      )
    )
  }

set.seed(42)
fits_diabetes_tree_2 <-
  grid_methods_tree %>%
  group_by(idx_method, method_desc) %>% 
  nest() %>% 
  mutate(
    fit = 
      purrr::map(data, 
                 ~fit_caret_tree(method = .x$method, preproc = .x$preproc))
  ) %>% 
  ungroup()
fits_diabetes_tree_2

## # A tibble: 6 x 4
##   idx_method method_desc                         data           fit       
##        <int> <chr>                               <list>         <list>    
## 1          1 {rpart} CART, Scaled                <tibble [1 x ~ <S3: trai~
## 2          2 {rpart} CART, Unscaled              <tibble [1 x ~ <S3: trai~
## 3          3 {randomForest} Random Forest, Scal~ <tibble [1 x ~ <S3: trai~
## 4          4 {randomForest} Random Forest, Unsc~ <tibble [1 x ~ <S3: trai~
## 5          5 {ranger} Random Forest, Scaled      <tibble [1 x ~ <S3: trai~
## 6          6 {ranger} Random Forest, Unscaled    <tibble [1 x ~ <S3: trai~

Cool! This approach complies with the modern split-apply-combine approach—dplyr::group_by() + tidyr::nest(), dplyr::mutate() + purrr::map() and tidyr::unnest()—and achieves the results which I sought.

Quantifying Model Quality

So I’ve got the fitted models for “many models” in a single tibble. How do I extract the results from this? {purrr}’s pluck() function is helpful here, along with the dplyr::mutate(), purrr::map(), and tidyr::unnest() functions used before.

unnest_caret_results <-
  function(fit, na.rm = TRUE) {
    fit %>%
      dplyr::mutate(results = map(fit, ~pluck(.x, "results"))) %>% 
      unnest(results, .drop = TRUE)
  }

We get the same exact results with both approaches demonstrated above, so I’ll only show the results for one here.

summ_diabetes_tree <-
  fits_diabetes_tree_2 %>%
  unnest_caret_results() %>%
  select(-matches("SD")) %>%
  arrange(desc(Accuracy))
summ_diabetes_tree

## # A tibble: 20 x 8
##    idx_method method_desc    cp Accuracy  Kappa  mtry splitrule
##         <int> <chr>       <dbl>    <dbl>  <dbl> <dbl> <chr>    
##  1          4 {randomFor~ NA      0.7734 0.4881     5 <NA>     
##  2          5 {ranger} R~ NA      0.7669 0.4713     5 gini     
##  3          5 {ranger} R~ NA      0.7669 0.4687     3 gini     
##  4          6 {ranger} R~ NA      0.7643 0.4686     3 gini     
##  5          6 {ranger} R~ NA      0.7631 0.4694     7 gini     
##  6          6 {ranger} R~ NA      0.7630 0.4666     5 gini     
##  7          3 {randomFor~ NA      0.7630 0.4632     3 <NA>     
##  8          4 {randomFor~ NA      0.7630 0.4661     7 <NA>     
##  9          5 {ranger} R~ NA      0.7629 0.4639     7 gini     
## 10          3 {randomFor~ NA      0.7617 0.4615     7 <NA>     
## 11          3 {randomFor~ NA      0.7591 0.4569     5 <NA>     
## 12          4 {randomFor~ NA      0.7578 0.4520     3 <NA>     
## 13          2 {rpart} CA~  0.01   0.7501 0.4311    NA <NA>     
## 14          1 {rpart} CA~  0.01   0.7396 0.4144    NA <NA>     
## 15          1 {rpart} CA~  0.1    0.7382 0.3794    NA <NA>     
## 16          2 {rpart} CA~  0.1    0.7240 0.3696    NA <NA>     
## 17          1 {rpart} CA~  1      0.6510 0         NA <NA>     
## 18          1 {rpart} CA~ 10      0.6510 0         NA <NA>     
## 19          2 {rpart} CA~  1      0.6510 0         NA <NA>     
## 20          2 {rpart} CA~ 10      0.6510 0         NA <NA>     
## # ... with 1 more variable: min.node.size <dbl>

And, with the results fashioned like this, we can easily perform other typical {dplyr} actions to gain insight from the results quickly.

summ_diabetes_bymethod <-
  summ_diabetes_tree %>% 
  group_by(idx_method, method_desc) %>% 
  summarise_at(vars(Accuracy), funs(min, max, mean, n = n())) %>% 
  ungroup() %>% 
  arrange(desc(max))
summ_diabetes_bymethod

## # A tibble: 6 x 6
##   idx_method method_desc                           min    max   mean     n
##        <int> <chr>                               <dbl>  <dbl>  <dbl> <int>
## 1          4 {randomForest} Random Forest, Uns~ 0.7578 0.7734 0.7647     3
## 2          5 {ranger} Random Forest, Scaled     0.7629 0.7669 0.7656     3
## 3          6 {ranger} Random Forest, Unscaled   0.7630 0.7643 0.7635     3
## 4          3 {randomForest} Random Forest, Sca~ 0.7591 0.7630 0.7613     3
## 5          2 {rpart} CART, Unscaled             0.6510 0.7501 0.6940     4
## 6          1 {rpart} CART, Scaled               0.6510 0.7396 0.6950     4

And let’s not forget about visualizing the results.

Conclusion

That’s it for this tutorial. I hope that this is useful for others. (If nothing else, it’s useful for me to review.) While the {caret} package does allow users to create custom train() functions, I believe that this functionality is typically beyond what a user needs when experimenting with different approaches (and can be quite complex). I believe that the approach (primarily the second one) that I’ve shown in this post offers a great amount of flexibility that complements the many other aspects of {caret}’s user-friendly, dynamic API.

In an actual analysis, the approach(es) that I’ve shown can be extremely useful in experimenting with many different methods, parameters, and data pre-processing in order to identify a set that is most appropriate for the context.