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Model Ensembles#

Ensemble learning is when multiple estimators are used together to form the prediction of a sample. Model ensembles can consist of multiple variations of the same estimator, a heterogeneous mix of estimators of the same type, or even a mix of different estimator types.

Bootstrap Aggregator#

Bootstrap Aggregation or bagging is a technique that trains multiple clones of the same estimator that each specialize on a subset of the training set known as a bootstrap set. The final prediction is the averaged prediction returned by the ensemble. By averaging, we can often achieve greater accuracy than a single estimator at the cost of training more models. In the example below, we'll wrap a Regression Tree in the Bootstrap Aggregator meta-estimator to form a forest of 1,000 trees. Calling the train() method will train the ensemble and afterward the meta-estimator can be used to make predictions like a regular estimator.

use Rubix\ML\BootstrapAggregator;
use Rubix\ML\Regressors\RegressionTree;

$estimator = new BootstrapAggregator(new RegressionTree(5), 1000);


Committee Machine#

Committee Machine is another ensemble learner that works by the principal of averaging. It is a meta-estimator consisting of a heterogeneous mix of estimators (referred to as experts) with user-programmable influences. Each expert is trained on the same dataset and the final prediction is based on the contribution of each expert weighted by their influence in the committee. By varying the influences of the experts, we can control which estimators contribute more or less to the final prediction.

use Rubix\ML\CommitteeMachine;
use Rubix\ML\RandomForest;
new Rubix\ML\SoftmaxClassifier;
use Rubix\ML\AdaBoost;

$estimator = new CommitteeMachine([
    new RandomForest(),
    new SoftmaxClassifier(128),
    new AdaBoost(),
], [
    3.0, 1.7, 2.5,

Model Chaining#

Model chaining is a form of ensemble learning that uses the predictions of one or more estimators as the input features to other downstream estimators. In this simple example, let's say we want to predict if we should give a customer a loan or not. One thing we could do is we could first predict the customer's credit score and then add it to the dataset with the original features for the loan classifier to train and infer on. We'll write a custom callback function to add the new feature to the training set after their values have been predicted using the Lambda Function transformer. The callback accepts three arguments - the current sample passed by reference, the current row offset, and a context variable which we'll use to store the predicted credit scores.

use Rubix\ML\Regressors\KDNeighborsRegressor;
use Rubix\ML\Transformers\LambdaFunction;
use Rubix\ML\Classifiers\RandomForest;
use Rubix\ML\Classifiers\ExtraTreeClassifier;

$creditScoreEstimator = new KDNeighborsRegressor(10);


$creditScores = $creditScoreEstimator->predict($dataset);

$addFeature = function (&$sample, $offset, $context) {
    $sample[] = $context[$offset];

$dataset->apply(new LambdaFunction($addFeature, $creditScores));

$loanApprovalEstimator = new RandomForest(new ExtraTreeClassifier(8), 300);


Model Orchestra#

When you combine chaining with model averaging you get a technique referred to as stacking. Unlike Committee Machine, which relies on a priori knowledge of the estimator influences, stacking aims to learn the influence scores automatically by using another model. We introduce the orchestra pattern for implementing a stacked model ensemble. The complete model consists of three Probabilistic classifiers referred to as the orchestra and a conductor that makes the final prediction by training on the class probabilities outputted by the orchestra. A key step to this process is to separate the training set into two sets so that we can do a second optimization to determine the model influences. We can vary the amount of data used to train each layer of the model by changing the proportion argument to the stratifiedSplit() method. For this example, we'll choose to use half of the data to train the orchestra and half to train the conductor.

use Rubix\ML\Classifiers\KDNeighbors;
use Rubix\ML\Classifiers\RadiusNeighbors;
use Rubix\ML\Classifiers\AdaBoost;
use Rubix\ML\Classifiers\MultilayerPerceptron;
use Rubix\ML\NeuralNet\Layers\Dense;
use Rubix\ML\NeuralNet\Layers\Activation;
use Rubix\ML\NeuralNet\ActivationFunctions\ReLU;
use Rubix\ML\Datasets\Labeled;

[$dataset1, $dataset2] = $training->stratifiedSplit(0.5);

$orchestra = [
    new KDNeighbors(10),
    new RadiusNeighbors(2.0),
    new AdaBoost(),

$samples = [];

foreach ($orchestra as $estimator) {

    $probabilities = $estimator->proba($dataset2);

    foreach ($probabilities as $offset => $dist) {
        $sample = &$sample[$offset];

        $sample = array_merge($sample, array_values($dist));

$dataset = new Labeled($samples, $dataset2->labels());

$conductor = new MultilayerPerceptron([
    new Dense(100),
    new Activation(new ReLU()),