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Basic Examples

Source: vignettes/articles/Basic-Examples.Rmd
Basic-Examples.Rmd

Let’s start with an extremely simple example: a prediction problem on a continuous outcome, where we want to use cross-validation to minimize the expected risk/loss on held out data across a few different models.

We’ll use the iris dataset to do this.

nadir::super_learner() strives to keep the syntax simple, so the simplest call to super_learner() might look something like this:

super_learner(
  data = iris,
  formula = Petal.Width ~ Petal.Length + Sepal.Length + Sepal.Width,
  learners = list(lnr_lm, lnr_rf, lnr_earth, lnr_mean))
#> function(newdata) {
#>     # for each model, predict on the newdata and apply the model weights
#>     parallel_lapply(1:length(fit_learners), function(i) {
#>       fit_learners[[i]](newdata) * learner_weights[[i]]
#>     }) |>
#>       Reduce(`+`, x = _) # aggregate across the weighted model predictions
#>   }
#> <bytecode: 0x1157b5c40>
#> <environment: 0x1157dcf28>
#> attr(,"class")
#> [1] "function"           "nadir_sl_predictor"

Notice what it returns: A function of newdata that predicts across the learners, sums up according to the learned weights, and returns the ensemble predictions.

We can store that learned predictor function and use it:

# We recommend storing more complicated arguments used repeatedly to simplify 
# the call to super_learner()
petal_formula <- Petal.Width ~ Petal.Length + Sepal.Length + Sepal.Width
learners <- list(lnr_lm, lnr_rf, lnr_earth, lnr_mean)

learned_sl_predictor <- super_learner(
  data = iris,
  formula = petal_formula,
  learners = learners)

In particular, we can use it to predict on the same dataset,

learned_sl_predictor(iris) |> head()
#>         1         2         3         4         5         6 
#> 0.2298699 0.1703070 0.1897956 0.2529110 0.2507371 0.3838603

On a random sample of it,

learned_sl_predictor(iris[sample.int(size = 10, n = nrow(iris)), ]) |> 
  head()
#>      130      138      141      150       65      118 
#> 1.947879 1.994989 2.060553 1.866126 1.186865 2.365248

Or on completely new data.

fake_iris_data <- data.frame()
fake_iris_data <- cbind.data.frame(
  Sepal.Length = 
  rnorm(
    n = 6,
    mean = mean(iris$Sepal.Length),
    sd = sd(iris$Sepal.Length)
  ),

Sepal.Width = 
  rnorm(
    n = 6,
    mean = mean(iris$Sepal.Width),
    sd = sd(iris$Sepal.Width)
  ),

Petal.Length = 
  rnorm(
    n = 6,
    mean = mean(iris$Petal.Length),
    sd = sd(iris$Petal.Length)
  )
)

learned_sl_predictor(fake_iris_data) |> 
  head()
#>         1         2         3         4         5         6 
#> 1.0684633 2.1233415 0.3412173 1.8459358 1.9028170 1.7436178

Getting More Information Out

Suppose we want to know a lot more about the super_learner() process, how it weighted the candidate learners, what the candidate learners predicted on the held-out data, etc., then we use the verbose_output = TRUE option.

sl_model_iris <- super_learner(
  data = iris,
  formula = petal_formula,
  learners = learners,
  verbose = TRUE)

str(sl_model_iris, max.level = 2)
#> List of 5
#>  $ sl_predictor       :function (newdata)  
#>   ..- attr(*, "srcref")= 'srcref' int [1:8] 448 39 454 3 39 3 2442 2448
#>   .. ..- attr(*, "srcfile")=Classes 'srcfilealias', 'srcfile' <environment: 0x115606d70> 
#>  $ y_variable         : chr "Petal.Width"
#>  $ outcome_type       : chr "continuous"
#>  $ learner_weights    : Named num [1:4] 0.588 0.412 0 0
#>   ..- attr(*, "names")= chr [1:4] "lm" "rf" "earth" "mean"
#>  $ holdout_predictions: tibble [150 × 6] (S3: tbl_df/tbl/data.frame)
#>  - attr(*, "class")= chr [1:2] "list" "nadir_sl_verbose_output"

To put some description to what’s contained in the verbose_output = TRUE output from super_learner():

  • A prediction function, $sl_predictor() that takes newdata
  • Some character fields like $y_variable and $outcome_type to provide some context to the learning task that was performed.
  • $learner_weights that indicate what weight the different candidate learners were given
  • $holdout_predictions: A data.frame of predictions from each of the candidate learners, along with the actual outcome from the held-out data.

We can call compare_learners() on the verbose output from super_learner() if we want to assess how the different learners performed. We can also call cv_super_learner() with the same arguments as super_learner() to wrap the super_learner() call in another layer of cross-validation to assess how super_learner() performs on held-out data.

compare_learners(sl_model_iris)
#> Inferring the loss metric for learner comparison based on the outcome type:
#> outcome_type=continuous -> using mean squared error
#> # A tibble: 1 × 4
#>       lm     rf earth  mean
#>    <dbl>  <dbl> <dbl> <dbl>
#> 1 0.0390 0.0454  1.70 0.612

cv_super_learner(
  data = iris, 
  formula = petal_formula,
  learners = learners)$cv_loss
#> The loss_metric is being inferred based on the outcome_type=continuous -> using CV-MSE
#> [1] 0.03496255

We can, of course, do anything with a super learned model that we would do with a conventional prediction model, like calculating performance statistics like R2R^2.

var_residuals <- var(iris$Sepal.Length - sl_model_iris$sl_predictor(iris))
total_variance <- var(iris$Sepal.Length)
variance_explained <- total_variance - var_residuals 

rsquared <- variance_explained / total_variance
print(rsquared)
#> [1] 0.7224058