A Brief Introduction to caretEnsemble

caretList

caretList is a flexible function for fitting many different caret models, with the same resampling parameters, to the same dataset. It returns a convenient list of caret objects which can later be passed to caretEnsemble and caretStack. caretList has almost exactly the same arguments as train (from the caret package), with the exception that the trControl argument comes last. It can handle both the formula interface and the explicit x, y interface to train. As in caret, the formula interface introduces some overhead and the x, y interface is preferred.

caretEnsemble has 2 arguments that can be used to specify which models to fit: methodList and tuneList. methodList is a simple character vector of methods that will be fit with the default train parameters, while tuneList can be used to customize the call to each component model and will be discussed in more detail later. First, lets build an example dataset (adapted from the caret vignette):

#Adapted from the caret vignette
library("caret")
library("mlbench")
library("pROC")
data(Sonar)
set.seed(107)
inTrain <- createDataPartition(y = Sonar$Class, p = .75, list = FALSE)
training <- Sonar[inTrain, ]
testing <- Sonar[-inTrain, ]
my_control <- trainControl(
  method="boot",
  number=25,
  savePredictions="final",
  classProbs=TRUE,
  index=createResample(training$Class, 25),
  summaryFunction=twoClassSummary
  )

Notice that we are explicitly setting the resampling index to being used in trainControl. If you do not set this index manually, caretList will attempt to set it for automatically, but it”s generally a good idea to set it yourself.

Now we can use caretList to fit a series of models (each with the same trControl):

library("rpart")
library("caretEnsemble")

## 
## Attaching package: 'caretEnsemble'

## The following object is masked from 'package:ggplot2':
## 
##     autoplot

model_list <- caretList(
  Class~., data=training,
  trControl=my_control,
  methodList=c("glm", "rpart")
  )

(As with train, the formula interface is convenient but introduces move overhead. For large datasets the explicitly passing x and y is preferred). We can use the predict function to extract predictions from this object for new data:

p <- as.data.frame(predict(model_list, newdata=head(testing)))
print(p)

If you desire more control over the model fit, use the caretModelSpec to construct a list of model specifications for the tuneList argument. This argument can be used to fit several different variants of the same model, and can also be used to pass arguments through train down to the component functions (e.g. trace=FALSE for nnet):

library("mlbench")
library("randomForest")
library("nnet")
model_list_big <- caretList(
  Class~., data=training,
  trControl=my_control,
  metric="ROC",
  methodList=c("glm", "rpart"),
  tuneList=list(
    rf1=caretModelSpec(method="rf", tuneGrid=data.frame(.mtry=2)),
    rf2=caretModelSpec(method="rf", tuneGrid=data.frame(.mtry=10), preProcess="pca"),
    nn=caretModelSpec(method="nnet", tuneLength=2, trace=FALSE)
  )
)

Finally, you should note that caretList does not support custom caret models. Fitting those models are beyond the scope of this vignette, but if you do so, you can manually add them to the model list (e.g. model_list_big[["my_custom_model"]] <- my_custom_model). Just be sure to use the same re-sampling indexes in trControl as you use in the caretList models!

caretEnsemble

caretList is the preferred way to construct list of caret models in this package, as it will ensure the resampling indexes are identical across all models. Lets take a closer look at our list of models:

xyplot(resamples(model_list))

As you can see from this plot, these 2 models are uncorrelated, and the rpart model is occasionally anti-predictive, with a one re-sample showing AUC of 0.46.

We can confirm the 2 model”s correlation with the modelCor function from caret (caret has a lot of convenient functions for analyzing lists of models):

modelCor(resamples(model_list))

##               glm       rpart
## glm    1.00000000 -0.01658742
## rpart -0.01658742  1.00000000

These 2 models make a good candidate for an ensemble: their predictions are fairly uncorrelated, but their overall accuracy is similar. We do a simple, linear greedy optimization on AUC using caretEnsemble:

greedy_ensemble <- caretEnsemble(
  model_list,
  metric="ROC",
  trControl=trainControl(
    number=2,
    summaryFunction=twoClassSummary,
    classProbs=TRUE
    ))
summary(greedy_ensemble)

## The following models were ensembled: glm, rpart 
## They were weighted: 
## 1.3764 -1.0734 -1.8211
## The resulting ROC is: 0.7379
## The fit for each individual model on the ROC is: 
##  method       ROC      ROCSD
##     glm 0.6884429 0.08365065
##   rpart 0.7013261 0.05304238

The ensemble”s AUC on the training set resamples is 0.76, which is about 7% better than the best individual model. We can confirm this finding on the test set:

library("caTools")
model_preds <- lapply(model_list, predict, newdata=testing, type="prob")
model_preds <- lapply(model_preds, function(x) x[, "M"])
model_preds <- data.frame(model_preds)
ens_preds <- predict(greedy_ensemble, newdata=testing, type="prob")
model_preds$ensemble <- ens_preds
caTools::colAUC(model_preds, testing$Class)

##               glm     rpart  ensemble
## M vs. R 0.7137346 0.7746914 0.8140432

The ensemble”s AUC on the test set is about 6% higher than the best individual model.

We can also use varImp to extract the variable importances from each member of the ensemble, as well as the final ensemble model:

varImp(greedy_ensemble)

(The columns each sum up to 100.)

caretStack

caretStack allows us to move beyond simple blends of models to using “meta-models” to ensemble collections of predictive models. DO NOT use the trainControl object you used to fit the training models to fit the ensemble. The re-sampling indexes will be wrong. Fortunately, you don”t need to be fastidious with re-sampling indexes for caretStack, as it only fits one model, and the defaults train uses will usually work fine:

glm_ensemble <- caretStack(
  model_list,
  method="glm",
  metric="ROC",
  trControl=trainControl(
    method="boot",
    number=10,
    savePredictions="final",
    classProbs=TRUE,
    summaryFunction=twoClassSummary
  )
)
model_preds2 <- model_preds
model_preds2$ensemble <- predict(glm_ensemble, newdata=testing, type="prob")
CF <- coef(glm_ensemble$ens_model$finalModel)[-1]
colAUC(model_preds2, testing$Class)

##               glm     rpart  ensemble
## M vs. R 0.7137346 0.7746914 0.8140432

CF/sum(CF)

##       glm     rpart 
## 0.3708346 0.6291654

Note that glm_ensemble$ens_model is a regular caret object of class train. The glm-weighted model weights (glm vs rpart) and test-set AUCs are extremely similar to the caretEnsemble greedy optimization.

We can also use more sophisticated ensembles than simple linear weights, but these models are much more susceptible to over-fitting, and generally require large sets of resamples to train on (n=50 or higher for bootstrap samples). Lets try one anyways:

library("gbm")
gbm_ensemble <- caretStack(
  model_list,
  method="gbm",
  verbose=FALSE,
  tuneLength=10,
  metric="ROC",
  trControl=trainControl(
    method="boot",
    number=10,
    savePredictions="final",
    classProbs=TRUE,
    summaryFunction=twoClassSummary
  )
)
model_preds3 <- model_preds
model_preds3$ensemble <- predict(gbm_ensemble, newdata=testing, type="prob")
colAUC(model_preds3, testing$Class)

##               glm     rpart  ensemble
## M vs. R 0.7137346 0.7746914 0.8009259

In this case, the sophisticated ensemble is no better than a simple weighted linear combination. Non-linear ensembles seem to work best when you have:

1. Lots of data.
2. Lots of models with similar accuracies.
3. Your models are uncorrelated: each one seems to capture a different aspect of the data, and different models perform best on different subsets of the data.