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= Bagging

Bagging stands for bootstrap aggregation. One way to reduce the variance of an estimate is to average together multiple estimates. For example, we can train M different trees on different subsets of the data (chosen randomly with replacement) and compute the ensemble:

image::images/bagging.png[]

Bagging uses bootstrap sampling to obtain the data subsets for training the base learners. For aggregating the outputs of base learners, bagging uses voting for classification and averaging for regression.


[source, java]
----
// Define the weak classifier.
DecisionTreeClassificationTrainer trainer = new DecisionTreeClassificationTrainer(5, 0);

// Set up the bagging process.
BaggedTrainer<Double> baggedTrainer = TrainerTransformers.makeBagged(
  trainer, // Trainer for making bagged
  10,      // Size of ensemble
  0.6,     // Subsample ratio to whole dataset
  4,       // Feature vector dimensionality
  3,       // Feature subspace dimensionality
  new OnMajorityPredictionsAggregator())
  .withEnvironmentBuilder(LearningEnvironmentBuilder
                          .defaultBuilder()
                          .withRNGSeed(1)
                         );

// Train the Bagged Model.
BaggedModel mdl = baggedTrainer.fit(
  ignite,
  dataCache,
  vectorizer
);
----


TIP: A commonly used class of ensemble algorithms are forests of randomized trees.

== Example

The full example could be found as a part of the Titanic tutorial https://github.com/apache/ignite/blob/master/examples/src/main/java/org/apache/ignite/examples/ml/tutorial/Step_10_Bagging.java[here].