In this article, we’ll be working through an example of the workflow of model stacking with the stacks package. At a high level, the workflow looks something like this:

The package is closely integrated with the rest of the functionality in tidymodels—we’ll load those packages as well, in addition to some tidyverse packages to evaluate our results later on.

In this example, we’ll make use of the tree_frogs data exported with stacks, giving experimental results on hatching behavior of red-eyed tree frog embryos!

Red-eyed tree frog (RETF) embryos can hatch earlier than their normal 7ish days if they detect potential predator threat. Researchers wanted to determine how, and when, these tree frog embryos were able to detect stimulus from their environment. To do so, they subjected the embryos at varying developmental stages to “predator stimulus” by jiggling the embryos with a blunt probe. Beforehand, though some of the embryos were treated with gentamicin, a compound that knocks out their lateral line (a sensory organ.) Researcher Julie Jung and her crew found that these factors inform whether an embryo hatches prematurely or not!

We’ll start out with predicting latency (i.e. time to hatch) based on other attributes. We’ll need to filter out NAs (i.e. cases where the embryo did not hatch) first.

Taking a quick look at the data, it seems like the hatch time is pretty closely related to some of our predictors!

Define candidate ensemble members

At the highest level, ensembles are formed from model definitions. In this package, model definitions are an instance of a minimal workflow, containing a model specification (as defined in the parsnip package) and, optionally, a preprocessor (as defined in the recipes package). Model definitions specify the form of candidate ensemble members.

A diagram representing 'model definitions,' which specify the form of candidate ensemble members. Three colored boxes represent three different model types; a K-nearest neighbors model (in salmon), a linear regression model (in yellow), and a support vector machine model (in green).

Defining the constituent model definitions is undoubtedly the longest part of building an ensemble with stacks. If you’re familiar with tidymodels “proper,” you’re probably fine to skip this section, keeping a few things in mind:

You’ll need to save the assessment set predictions and workflow utilized in your tune_grid(), tune_bayes(), or fit_resamples() objects by setting the control arguments save_pred = TRUE and save_workflow = TRUE. Note the use of the control_stack_*() convenience functions below!
Each model definition must share the same rsample rset object.

We’ll first start out with splitting up the training data, generating resamples, and setting some options that will be used by each model definition.

# some setup: resampling and a basic recipe
set.seed(1)
tree_frogs_split <- initial_split(tree_frogs)
tree_frogs_train <- training(tree_frogs_split)
tree_frogs_test  <- testing(tree_frogs_split)

set.seed(1)
folds <- rsample::vfold_cv(tree_frogs_train, v = 5)

tree_frogs_rec <- 
  recipe(latency ~ ., data = tree_frogs_train)

metric <- metric_set(rmse)

Tuning and fitting results for use in ensembles need to be fitted with the control arguments save_pred = TRUE and save_workflow = TRUE—these settings ensure that the assessment set predictions, as well as the workflow used to fit the resamples, are stored in the resulting object. For convenience, stacks supplies some control_stack_*() functions to generate the appropriate objects for you.

In this example, we’ll be working with tune_grid() and fit_resamples() from the tune package, so we will use the following control settings:

ctrl_grid <- control_stack_grid()
ctrl_res <- control_stack_resamples()

We’ll define three different model definitions to try to predict time to hatch—a K-nearest neighbors model (with hyperparameters to tune), a linear model, and a support vector machine model (again, with hyperparameters to tune).

Starting out with K-nearest neighbors, we begin by creating a parsnip model specification:

# create a model definition
knn_spec <-
  nearest_neighbor(
    mode = "regression", 
    neighbors = tune("k")
  ) %>%
  set_engine("kknn")

knn_spec
#> K-Nearest Neighbor Model Specification (regression)
#> 
#> Main Arguments:
#>   neighbors = tune("k")
#> 
#> Computational engine: kknn

Note that, since we are tuning over several possible numbers of neighbors, this model specification defines multiple model configurations. The specific form of those configurations will be determined when specifying the grid search in tune_grid().

From here, we extend the basic recipe defined earlier to fully specify the form of the design matrix for use in a K-nearest neighbors model:

# extend the recipe
knn_rec <-
  tree_frogs_rec %>%
  step_dummy(all_nominal_predictors()) %>%
  step_zv(all_predictors()) %>%
  step_impute_mean(all_numeric_predictors()) %>%
  step_normalize(all_numeric_predictors())

knn_rec
#> Recipe
#> 
#> Inputs:
#> 
#>       role #variables
#>    outcome          1
#>  predictor          4
#> 
#> Operations:
#> 
#> Dummy variables from all_nominal_predictors()
#> Zero variance filter on all_predictors()
#> Mean imputation for all_numeric_predictors()
#> Centering and scaling for all_numeric_predictors()

Starting with the basic recipe, we convert categorical variables to dummy variables, remove column with only one observation, impute missing values in numeric variables using the mean, and normalize numeric predictors. Pre-processing instructions for the remaining models are defined similarly.

Now, we combine the model specification and pre-processing instructions defined above to form a workflow object:

# add both to a workflow
knn_wflow <- 
  workflow() %>% 
  add_model(knn_spec) %>%
  add_recipe(knn_rec)

knn_wflow
#> ══ Workflow ════════════════════════════════════════════════════════════════════
#> Preprocessor: Recipe
#> Model: nearest_neighbor()
#> 
#> ── Preprocessor ────────────────────────────────────────────────────────────────
#> 4 Recipe Steps
#> 
#> • step_dummy()
#> • step_zv()
#> • step_impute_mean()
#> • step_normalize()
#> 
#> ── Model ───────────────────────────────────────────────────────────────────────
#> K-Nearest Neighbor Model Specification (regression)
#> 
#> Main Arguments:
#>   neighbors = tune("k")
#> 
#> Computational engine: kknn

Finally, we can make use of the workflow, training set resamples, metric set, and control object to tune our hyperparameters. Using the grid argument, we specify that we would like to optimize over four possible values of k using a grid search.

# tune k and fit to the 5-fold cv
set.seed(2020)
knn_res <- 
  tune_grid(
    knn_wflow,
    resamples = folds,
    metrics = metric,
    grid = 4,
    control = ctrl_grid
  )

knn_res
#> # Tuning results
#> # 5-fold cross-validation 
#> # A tibble: 5 × 5
#>   splits           id    .metrics         .notes           .predictions      
#>   <list>           <chr> <list>           <list>           <list>            
#> 1 <split [343/86]> Fold1 <tibble [4 × 5]> <tibble [0 × 3]> <tibble [344 × 5]>
#> 2 <split [343/86]> Fold2 <tibble [4 × 5]> <tibble [0 × 3]> <tibble [344 × 5]>
#> 3 <split [343/86]> Fold3 <tibble [4 × 5]> <tibble [0 × 3]> <tibble [344 × 5]>
#> 4 <split [343/86]> Fold4 <tibble [4 × 5]> <tibble [0 × 3]> <tibble [344 × 5]>
#> 5 <split [344/85]> Fold5 <tibble [4 × 5]> <tibble [0 × 3]> <tibble [340 × 5]>

This knn_res object fully specifies the candidate members, and is ready to be included in a stacks workflow.

Now, specifying the linear model, note that we are not optimizing over any hyperparameters. Thus, we use the fit_resamples() function rather than tune_grid() or tune_bayes() when fitting to our resamples.

# create a model definition
lin_reg_spec <-
  linear_reg() %>%
  set_engine("lm")

# extend the recipe
lin_reg_rec <-
  tree_frogs_rec %>%
  step_dummy(all_nominal_predictors()) %>%
  step_zv(all_predictors())

# add both to a workflow
lin_reg_wflow <- 
  workflow() %>%
  add_model(lin_reg_spec) %>%
  add_recipe(lin_reg_rec)

# fit to the 5-fold cv
set.seed(2020)
lin_reg_res <- 
  fit_resamples(
    lin_reg_wflow,
    resamples = folds,
    metrics = metric,
    control = ctrl_res
  )

lin_reg_res
#> # Resampling results
#> # 5-fold cross-validation 
#> # A tibble: 5 × 5
#>   splits           id    .metrics         .notes           .predictions     
#>   <list>           <chr> <list>           <list>           <list>           
#> 1 <split [343/86]> Fold1 <tibble [1 × 4]> <tibble [0 × 3]> <tibble [86 × 4]>
#> 2 <split [343/86]> Fold2 <tibble [1 × 4]> <tibble [0 × 3]> <tibble [86 × 4]>
#> 3 <split [343/86]> Fold3 <tibble [1 × 4]> <tibble [0 × 3]> <tibble [86 × 4]>
#> 4 <split [343/86]> Fold4 <tibble [1 × 4]> <tibble [0 × 3]> <tibble [86 × 4]>
#> 5 <split [344/85]> Fold5 <tibble [1 × 4]> <tibble [0 × 3]> <tibble [85 × 4]>

Finally, putting together the model definition for the support vector machine:

# create a model definition
svm_spec <- 
  svm_rbf(
    cost = tune("cost"), 
    rbf_sigma = tune("sigma")
  ) %>%
  set_engine("kernlab") %>%
  set_mode("regression")

# extend the recipe
svm_rec <-
  tree_frogs_rec %>%
  step_dummy(all_nominal_predictors()) %>%
  step_zv(all_predictors()) %>%
  step_impute_mean(all_numeric_predictors()) %>%
  step_corr(all_predictors()) %>%
  step_normalize(all_numeric_predictors())

# add both to a workflow
svm_wflow <- 
  workflow() %>% 
  add_model(svm_spec) %>%
  add_recipe(svm_rec)

# tune cost and sigma and fit to the 5-fold cv
set.seed(2020)
svm_res <- 
  tune_grid(
    svm_wflow, 
    resamples = folds, 
    grid = 6,
    metrics = metric,
    control = ctrl_grid
  )

svm_res
#> # Tuning results
#> # 5-fold cross-validation 
#> # A tibble: 5 × 5
#>   splits           id    .metrics         .notes           .predictions      
#>   <list>           <chr> <list>           <list>           <list>            
#> 1 <split [343/86]> Fold1 <tibble [6 × 6]> <tibble [0 × 3]> <tibble [516 × 6]>
#> 2 <split [343/86]> Fold2 <tibble [6 × 6]> <tibble [0 × 3]> <tibble [516 × 6]>
#> 3 <split [343/86]> Fold3 <tibble [6 × 6]> <tibble [0 × 3]> <tibble [516 × 6]>
#> 4 <split [343/86]> Fold4 <tibble [6 × 6]> <tibble [0 × 3]> <tibble [516 × 6]>
#> 5 <split [344/85]> Fold5 <tibble [6 × 6]> <tibble [0 × 3]> <tibble [510 × 6]>

Altogether, we’ve created three model definitions, where the K-nearest neighbors model definition specifies 4 model configurations, the linear regression specifies 1, and the support vector machine specifies 6.

A diagram representing 'candidate members' generated from each model definition. Four salmon-colored boxes labeled 'KNN' represent K-nearest neighbors models trained on the resamples with differing hyperparameters. Similarly, the linear regression (LM) model generates one candidate member, and the support vector machine (SVM) model generates six.

With these three model definitions fully specified, we are ready to begin stacking these model configurations. (Note that, in most applied settings, one would likely specify many more than 11 candidate members.)

Putting together a stack

The first step to building an ensemble with stacks is to create a data_stack object—in this package, data stacks are tibbles (with some extra attributes) that contain the assessment set predictions for each candidate ensemble member.

We can initialize a data stack using the stacks() function.

stacks()
#> # A data stack with 0 model definitions and 0 candidate members.

The stacks() function works sort of like the ggplot() constructor from ggplot2—the function creates a basic structure that the object will be built on top of—except you’ll pipe the outputs rather than adding them with +.

The add_candidates() function adds ensemble members to the stack.

tree_frogs_data_st <- 
  stacks() %>%
  add_candidates(knn_res) %>%
  add_candidates(lin_reg_res) %>%
  add_candidates(svm_res)

tree_frogs_data_st
#> # A data stack with 3 model definitions and 11 candidate members:
#> #   knn_res: 4 model configurations
#> #   lin_reg_res: 1 model configuration
#> #   svm_res: 6 model configurations
#> # Outcome: latency (numeric)

As mentioned before, under the hood, a data_stack object is really just a tibble with some extra attributes. Checking out the actual data:

as_tibble(tree_frogs_data_st)
#> # A tibble: 429 × 12
#>    latency knn_res_1_1 knn_res…¹ knn_r…² knn_r…³ lin_r…⁴ svm_r…⁵ svm_r…⁶ svm_r…⁷
#>      <dbl>       <dbl>     <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#>  1     142        76.5      67.8    83.2    83.0   114.     71.0    71.0    84.6
#>  2      79        74.3      71.0    64.2    63.9    78.6    72.5    72.5    71.4
#>  3      50        75.0      71.4    64.9    64.3    81.5    71.0    71.0    70.6
#>  4      68        47.9      49.7    54.0    54.0    78.6    71.1    71.1    70.4
#>  5      64        60.9      53.1    48.4    48.3    36.5    71.0    71.0    51.5
#>  6      52       207.      168.    129.    124.    124.     71.1    71.1    92.1
#>  7      39        30.8      29.1    32.7    33.0    35.2    72.5    72.5    50.6
#>  8      46        32.3      31.1    35.0    34.6    37.1    72.5    72.5    51.2
#>  9     137        75.9      78.8    90.4    90.6    78.8    71.1    71.1    70.6
#> 10      73        67.7      73.6    67.9    67.4    38.8    72.5    72.5    51.7
#> # … with 419 more rows, 3 more variables: svm_res_1_5 <dbl>, svm_res_1_2 <dbl>,
#> #   svm_res_1_6 <dbl>, and abbreviated variable names ¹knn_res_1_2,
#> #   ²knn_res_1_3, ³knn_res_1_4, ⁴lin_reg_res_1_1, ⁵svm_res_1_1, ⁶svm_res_1_4,
#> #   ⁷svm_res_1_3

The first column gives the first response value, and the remaining columns give the assessment set predictions for each ensemble member. Since we’re in the regression case, there’s only one column per ensemble member. In classification settings, there are as many columns as there are levels of the outcome variable per candidate ensemble member.

That’s it! We’re now ready to evaluate how it is that we need to combine predictions from each candidate ensemble member.

Fit the stack

The outputs from each of these candidate ensemble members are highly correlated, so the blend_predictions() function performs regularization to figure out how we can combine the outputs from the stack members to come up with a final prediction.

tree_frogs_model_st <-
  tree_frogs_data_st %>%
  blend_predictions()

The blend_predictions function determines how member model output will ultimately be combined in the final prediction by fitting a LASSO model on the data stack, predicting the true assessment set outcome using the predictions from each of the candidate members. Candidates with nonzero stacking coefficients become members.

A diagram representing 'stacking coefficients,' the coefficients of the linear model combining each of the candidate member predictions to generate the ensemble's ultimate prediction. Boxes for each of the candidate members are placed besides each other, filled in with color if the coefficient for the associated candidate member is nonzero.

To make sure that we have the right trade-off between minimizing the number of members and optimizing performance, we can use the autoplot() method:

autoplot(tree_frogs_model_st)

To show the relationship more directly:

autoplot(tree_frogs_model_st, type = "members")

If these results were not good enough, blend_predictions() could be called again with different values of penalty. As it is, blend_predictions() picks the penalty parameter with the numerically optimal results. To see the top results:

autoplot(tree_frogs_model_st, type = "weights")

A ggplot bar plot, giving the stacking coefficient on the x axis and member on the y axis. There are three members in this ensemble, where a nearest neighbor is weighted most heavily, followed by a linear regression with a stacking coefficient about half as large, followed by a support vector machine with a very small contribution.

Now that we know how to combine our model output, we can fit the candidates with non-zero stacking coefficients on the full training set.

tree_frogs_model_st <-
  tree_frogs_model_st %>%
  fit_members()

A diagram representing the ensemble members, where each are pentagons labeled and colored-in according to the candidate members they arose from.

Model stacks can be thought of as a group of fitted member models and a set of instructions on how to combine their predictions.

A diagram representing the 'model stack' class, which collates the stacking coefficients and members (candidate members with nonzero stacking coefficients that are trained on the full training set). The representation of the stacking coefficients and members is as before. Model stacks are a list subclass.

To identify which model configurations were assigned what stacking coefficients, we can make use of the collect_parameters() function:

collect_parameters(tree_frogs_model_st, "svm_res")
#> # A tibble: 6 × 4
#>   member         cost    sigma  coef
#>   <chr>         <dbl>    <dbl> <dbl>
#> 1 svm_res_1_1 0.00143 6.64e- 9 0    
#> 2 svm_res_1_2 3.59    3.95e- 4 0.422
#> 3 svm_res_1_3 0.0978  1.81e- 2 0.459
#> 4 svm_res_1_4 0.00849 2.16e-10 0    
#> 5 svm_res_1_5 0.256   4.54e- 1 0.168
#> 6 svm_res_1_6 7.64    3.16e- 7 0

This object is now ready to predict with new data!

tree_frogs_test <- 
  tree_frogs_test %>%
  bind_cols(predict(tree_frogs_model_st, .))

Juxtaposing the predictions with the true data:

ggplot(tree_frogs_test) +
  aes(x = latency, 
      y = .pred) +
  geom_point() + 
  coord_obs_pred()

A ggplot scatterplot showing observed versus predicted latency values. While there is indeed a positive and roughly linear relationship, there is certainly patterned structure in the residuals.

Looks like our predictions were pretty strong! How do the stacks predictions perform, though, as compared to the members’ predictions? We can use the type = "members" argument to generate predictions from each of the ensemble members.

member_preds <- 
  tree_frogs_test %>%
  select(latency) %>%
  bind_cols(predict(tree_frogs_model_st, tree_frogs_test, members = TRUE))

Now, evaluating the root mean squared error from each model:

map_dfr(member_preds, rmse, truth = latency, data = member_preds) %>%
  mutate(member = colnames(member_preds))
#> # A tibble: 7 × 4
#>   .metric .estimator .estimate member         
#>   <chr>   <chr>          <dbl> <chr>          
#> 1 rmse    standard         0   latency        
#> 2 rmse    standard        54.5 .pred          
#> 3 rmse    standard        56.2 knn_res_1_3    
#> 4 rmse    standard        55.5 lin_reg_res_1_1
#> 5 rmse    standard        60.4 svm_res_1_3    
#> 6 rmse    standard        56.8 svm_res_1_5    
#> 7 rmse    standard        61.2 svm_res_1_2

As we can see, the stacked ensemble outperforms each of the member models, though is closely followed by one of its members.

Voila! You’ve now made use of the stacks package to predict red-eyed tree frog embryo hatching using a stacked ensemble! The full visual outline for these steps can be found here.

Getting Started With stacks

Define candidate ensemble members

Putting together a stack

Fit the stack