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!
Let’s give this a go!
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.
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:
fit_resamples()objects by setting the
save_pred = TRUEand
save_workflow = TRUE. Note the use of the
control_stack_*()convenience functions below!
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.
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
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()) %>% step_zv(all_predictors(), skip = TRUE) %>% step_meanimpute(all_numeric(), skip = TRUE) %>% step_normalize(all_numeric(), skip = TRUE) #> Warning: `step_meanimpute()` was deprecated in recipes 0.1.16. #> Please use `step_impute_mean()` instead. knn_rec #> Data Recipe #> #> Inputs: #> #> role #variables #> outcome 1 #> predictor 4 #> #> Operations: #> #> Dummy variables from all_nominal() #> Zero variance filter on all_predictors() #> Mean Imputation for all_numeric() #> Centering and scaling for all_numeric()
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
# 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 x 5 #> splits id .metrics .notes .predictions #> <list> <chr> <list> <list> <list> #> 1 <split [343/86]> Fold1 <tibble [4 × 5]> <tibble [0 × 1]> <tibble [344 × 5]> #> 2 <split [343/86]> Fold2 <tibble [4 × 5]> <tibble [0 × 1]> <tibble [344 × 5]> #> 3 <split [343/86]> Fold3 <tibble [4 × 5]> <tibble [0 × 1]> <tibble [344 × 5]> #> 4 <split [343/86]> Fold4 <tibble [4 × 5]> <tibble [0 × 1]> <tibble [344 × 5]> #> 5 <split [344/85]> Fold5 <tibble [4 × 5]> <tibble [0 × 1]> <tibble [340 × 5]>
knn_res object fully specifies the candidate members, and is ready to be included in a
Now, specifying the linear model, note that we are not optimizing over any hyperparameters. Thus, we use the
fit_resamples() function rather than
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()) %>% step_zv(all_predictors(), skip = TRUE) # 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 x 5 #> splits id .metrics .notes .predictions #> <list> <chr> <list> <list> <list> #> 1 <split [343/86]> Fold1 <tibble [1 × 4]> <tibble [0 × 1]> <tibble [86 × 4]> #> 2 <split [343/86]> Fold2 <tibble [1 × 4]> <tibble [0 × 1]> <tibble [86 × 4]> #> 3 <split [343/86]> Fold3 <tibble [1 × 4]> <tibble [0 × 1]> <tibble [86 × 4]> #> 4 <split [343/86]> Fold4 <tibble [1 × 4]> <tibble [0 × 1]> <tibble [86 × 4]> #> 5 <split [344/85]> Fold5 <tibble [1 × 4]> <tibble [0 × 1]> <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()) %>% step_zv(all_predictors(), skip = TRUE) %>% step_meanimpute(all_numeric(), skip = TRUE) %>% step_corr(all_predictors(), skip = TRUE) %>% step_normalize(all_numeric(), skip = TRUE) #> Warning: `step_meanimpute()` was deprecated in recipes 0.1.16. #> Please use `step_impute_mean()` instead. # 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 x 5 #> splits id .metrics .notes .predictions #> <list> <chr> <list> <list> <list> #> 1 <split [343/86]> Fold1 <tibble [6 × 6]> <tibble [0 × 1]> <tibble [516 × 6]> #> 2 <split [343/86]> Fold2 <tibble [6 × 6]> <tibble [0 × 1]> <tibble [516 × 6]> #> 3 <split [343/86]> Fold3 <tibble [6 × 6]> <tibble [0 × 1]> <tibble [516 × 6]> #> 4 <split [343/86]> Fold4 <tibble [6 × 6]> <tibble [0 × 1]> <tibble [516 × 6]> #> 5 <split [344/85]> Fold5 <tibble [6 × 6]> <tibble [0 × 1]> <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.
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.)
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() #> # A data stack with 0 model definitions and 0 candidate members.
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
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 x 12 #> latency knn_res_1_1 knn_res_1_2 knn_res_1_3 knn_res_1_4 lin_reg_res_1_1 #> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> #> 1 142 -0.496 -0.478 -0.492 -0.494 114. #> 2 79 -0.381 -0.446 -0.542 -0.553 78.6 #> 3 50 -0.311 -0.352 -0.431 -0.438 81.5 #> 4 68 -0.312 -0.368 -0.463 -0.473 78.6 #> 5 64 -0.496 -0.478 -0.492 -0.494 36.5 #> 6 52 -0.391 -0.412 -0.473 -0.482 124. #> 7 39 -0.523 -0.549 -0.581 -0.587 35.2 #> 8 46 -0.523 -0.549 -0.581 -0.587 37.1 #> 9 137 -0.287 -0.352 -0.447 -0.456 78.8 #> 10 73 -0.523 -0.549 -0.581 -0.587 38.8 #> # … with 419 more rows, and 6 more variables: svm_res_1_1 <dbl>, #> # svm_res_1_4 <dbl>, svm_res_1_3 <dbl>, svm_res_1_5 <dbl>, svm_res_1_2 <dbl>, #> # svm_res_1_6 <dbl>
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.
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.
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.
To make sure that we have the right trade-off between minimizing the number of members and optimizing performance, we can use the
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")
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.
Model stacks can be thought of as a group of fitted member models and a set of instructions on how to combine their predictions.
To identify which model configurations were assigned what stacking coefficients, we can make use of the
collect_parameters(tree_frogs_model_st, "svm_res") #> # A tibble: 6 x 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 27.1 #> 3 svm_res_1_3 0.0978 1.81e- 2 0 #> 4 svm_res_1_4 0.00849 2.16e-10 0 #> 5 svm_res_1_5 0.256 4.54e- 1 0 #> 6 svm_res_1_6 7.64 3.16e- 7 352.
This object is now ready to predict with new data!
Juxtaposing the predictions with the true data:
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.
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: 6 x 4 #> .metric .estimator .estimate member #> <chr> <chr> <dbl> <chr> #> 1 rmse standard 0 latency #> 2 rmse standard 55.3 .pred #> 3 rmse standard 114. knn_res_1_4 #> 4 rmse standard 55.5 lin_reg_res_1_1 #> 5 rmse standard 114. svm_res_1_2 #> 6 rmse standard 114. svm_res_1_6
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.