In this demonstration, we will illustrate the basic functionality of the
sl3 R package. Specifically, we will walk through the concept of machine learning pipelines, the construction of ensemble models, simple optimality properties of stacked regression. After this introduction we will be well prepared to discuss more advanced topics in ensemble learning, such as optimal kernel density estimation.
First, we'll load the packages required for this exercise and load a simple data set (
cpp_imputed below) that we'll use for demonstration purposes:
set.seed(49753) # packages we'll be using library(data.table) library(SuperLearner) library(origami) library(sl3) # load example data set data(cpp_imputed) # take a peek at the data head(cpp_imputed)
Loading required package: nnls Super Learner Version: 2.0-23-9000 Package created on 2017-11-29 origami: Generalized Cross-Validation Framework Version: 1.0.0
To use this data set with
sl3, the object must be wrapped in a customized
sl3 container, an
sl3 "Task" object. A task is an idiom for all of the elements of a prediction problem other than the learning algorithms and prediction approach itself -- that is, a task delineates the structure of the data set of interest and any potential metadata (e.g., observation-level weights).
# here are the covariates we are interested in and, of course, the outcome covars <- c("apgar1", "apgar5", "parity", "gagebrth", "mage", "meducyrs", "sexn") outcome <- "haz" # create the sl3 task and take a look at it task <- make_sl3_Task(data = cpp_imputed, covariates = covars, outcome = outcome, outcome_type = "continuous") # let's take a look at the sl3 task task
A sl3 Task with 1441 obs and these nodes: $covariates  "apgar1" "apgar5" "parity" "gagebrth" "mage" "meducyrs" "sexn" $outcome  "haz" $id NULL $weights NULL $offset NULL
sl3 is designed using basic OOP principles and the
R6 OOP framework. While we’ve tried to make it easy to use
sl3 without worrying much about OOP, it is helpful to have some intuition about how
sl3 is structured. In this section, we briefly outline some key concepts from OOP. Readers familiar with OOP basics are invited to skip this section. The key concept of OOP is that of an object, a collection of data and functions that corresponds to some conceptual unit. Objects have two main types of elements: (1) fields, which can be thought of as nouns, are information about an object, and (2) methods, which can be thought of as verbs, are actions an object can perform. Objects are members of classes, which define what those specific fields and methods are. Classes can inherit elements from other classes (sometimes called base classes) – accordingly, classes that are similar, but not exactly the same, can share some parts of their definitions.
Many different implementations of OOP exist, with variations in how these concepts are implemented and used. R has several different implementations, including
S4, reference classes, and
sl3 uses the
R6 implementation. In
R6, methods and fields of a class object are accessed using the
$ operator. The next section explains how these concepts are used in
sl3 to model machine learning problems and algorithms.
Lrnr_base is the base class for defining machine learning algorithms, as well as fits for those algorithms to particular
sl3_Tasks. Different machine learning algorithms are defined in classes that inherit from
Lrnr_base. For instance, the
Lrnr_glm class inherits from
Lrnr_base, and defines a learner that fits generalized linear models. We will use the term learners to refer to the family of classes that inherit from
Lrnr_base. Learner objects can be constructed from their class definitions using the
# make learner object lrnr_glm <- make_learner(Lrnr_glm)
Because all learners inherit from
Lrnr_base, they have many features in common, and can be used interchangeably. All learners define three main methods:
chain. The first,
train, takes an
sl3_task object, and returns a
learner_fit, which has the same class as the learner that was trained:
# fit learner to task data lrnr_glm_fit <- lrnr_glm$train(task) # verify that the learner is fit lrnr_glm_fit$is_trained
Here, we fit the learner to the CPP task we defined above. Both
lrnr_glm_fit are objects of class
Lrnr_glm, although the former defines a learner and the latter defines a fit of that learner. We can distiguish between the learners and learner fits using the
is_trained field, which is true for fits but not for learners.
Now that we’ve fit a learner, we can generate predictions using the predict method:
# get learner predictions preds <- lrnr_glm_fit$predict() head(preds)
Here, we specified task as the task for which we wanted to generate predictions. If we had omitted this, we would have gotten the same predictions because predict defaults to using the task provided to train (called the training task). Alternatively, we could have provided a different task for which we want to generate predictions.
The final important learner method, chain, will be discussed below, in the section on learner composition. As with
sl3_Task, learners have a variety of fields and methods we haven’t discussed here. More information on these is available in the help for
A pipeline is a set of learners to be fit sequentially, where the fit from one learner is used to define the task for the next learner. There are many ways in which a learner can define the task for the downstream learner. The chain method defined by learners defines how this will work. Let’s look at the example of pre-screening variables. For now, we’ll rely on a screener from the
SuperLearner package, although native
sl3 screening algorithms will be implemented soon.
Below, we generate a screener object based on the
screen.corP and fit it to our task. Inspecting the fit, we see that it selected a subset of covariates:
screen_cor <- Lrnr_pkg_SuperLearner_screener$new("screen.corP") screen_fit <- screen_cor$train(task) print(screen_fit)
 "Lrnr_pkg_SuperLearner_screener_screen.corP" $selected  "parity" "gagebrth"
Pipeline class automates this process. It takes an arbitrary number of learners and fits them sequentially, training and chaining each one in turn. Since
Pipeline is a learner like any other, it shares the same interface. We can define a pipeline using
make_learner, and use
predict just as we did before:
sg_pipeline <- make_learner(Pipeline, screen_cor, lrnr_glm) sg_pipeline_fit <- sg_pipeline$train(task) sg_pipeline_preds <- sg_pipeline_fit$predict() head(sg_pipeline_preds)
Stacks combine multiple learners. Stacks train learners simultaneously, so that their predictions can be either combined or compared. Again,
Stack is just a special learner and so has the same interface as all other learners:
stack <- make_learner(Stack, lrnr_glm, sg_pipeline) stack_fit <- stack$train(task) stack_preds <- stack_fit$predict() head(stack_preds)
Above, we’ve defined and fit a stack comprised of a simple
glm learner as well as a pipeline that combines a screening algorithm with that same learner. We could have included any abitrary set of learners and pipelines, the latter of which are themselves just learners. We can see that the predict method now returns a matrix, with a column for each learner included in the stack.
Having defined a stack, we might want to compare the performance of learners in the stack, which we may do using cross-validation. The
Lrnr_cv learner wraps another learner and performs training and prediction in a cross-validated fashion, using separate training and validation splits as defined by
Below, we define a new
Lrnr_cv object based on the previously defined stack and train it and generate predictions on the validation set:
cv_stack <- Lrnr_cv$new(stack) cv_fit <- cv_stack$train(task) cv_preds <- cv_fit$predict()
risks <- cv_fit$cv_risk(loss_squared_error) print(risks)
Lrnr_glm 1.604769 Lrnr_pkg_SuperLearner_screener_screen.corP___Lrnr_glm 1.604186
We can combine all of the above elements,
Stacks, and cross-validation using
Lrnr_cv, to easily define a Super Learner. The Super Learner algorithm works by fitting a “meta-learner”, which combines predictions from multiple stacked learners. It does this while avoiding overfitting by training the meta-learner on validation-set predictions in a manner that is cross-validated. Using some of the objects we defined in the above examples, this becomes a very simple operation:
metalearner <- make_learner(Lrnr_nnls) cv_task <- cv_fit$chain() ml_fit <- metalearner$train(cv_task)
Here, we used a special learner, Lrnr_nnls, for the meta-learning step. This fits a non-negative least squares meta-learner. It is important to note that any learner can be used as a meta-learner.
The Super Learner finally produced is defined as a pipeline with the learner stack trained on the full data and the meta-learner trained on the validation-set predictions. Below, we use a special behavior of pipelines: if all objects passed to a pipeline are learner fits (i.e.,
TRUE), the result will also be a fit:
sl_pipeline <- make_learner(Pipeline, stack_fit, ml_fit) sl_preds <- sl_pipeline$predict() head(sl_preds)
An optimal stacked regression model (or Super Learner) may be fit in a more streamlined manner using the
Lrnr_sl learner. For simplicity, we will use the same set of learners and meta-learning algorithm as we did before:
sl <- Lrnr_sl$new(learners = stack, metalearner = metalearner) sl_fit <- sl$train(task) lrnr_sl_preds <- sl_fit$predict() head(lrnr_sl_preds)
We can see that this generates the same predictions as the more hands-on definition above.
Construct a Super Learner using $5$ (or more) learning algorithms, fit it on the training data given below (
task_train) , and obtain predictions on the held out set (
At least $2$ of the learners that you choose should be variations of a single learner, differentiated from one another solely by the use of different values for $1$ (or more) hyperparameters.
After fitting the Super Learner, identify the "discrete Super Learner".
# let's split the data into training and validation sets train_cpp_imputed <- as.data.table(cpp_imputed[sample(nrow(cpp_imputed), 0.75 * nrow(cpp_imputed)), ]) valid_cpp_imputed <- as.data.table(cpp_imputed[!(seq_len(nrow(cpp_imputed)) %in% rownames(train_cpp_imputed)), ]) # create the sl3 task and take a look at it task_train <- make_sl3_Task(data = train_cpp_imputed, covariates = covars, outcome = outcome, outcome_type = "continuous") task_train # we'll also create an sl3 task for the holdout set task_valid <- make_sl3_Task(data = valid_cpp_imputed, covariates = covars, outcome = outcome, outcome_type = "continuous")
A sl3 Task with 1080 obs and these nodes: $covariates  "apgar1" "apgar5" "parity" "gagebrth" "mage" "meducyrs" "sexn" $outcome  "haz" $id NULL $weights NULL $offset NULL