mlpack/doc/user/methods/random_forest.md

RandomForest

The RandomForest class implements a parallelized random forest classifier that supports numerical and categorical features, by default using Gini gain to choose which feature to split on in each tree.

Random forests are a collection of decision trees that give better performance than a single decision tree. They are useful for classifying points with discrete labels (i.e. 0, 1, 2). This implementation of the RandomForest class is not for regression (i.e. predicting continuous values).

mlpack's RandomForest class offers configurability via template parameters and runtime parameters. This is used to provide the additional API-compatible ExtraTrees class. To use ExtraTrees, simply replace RandomForest with ExtraTrees in any of the documentation below. (More information...)

Simple usage example:

// Train a random forest on random numeric data and predict labels on test data:

// All data and labels are uniform random; 10 dimensional data, 5 classes.
// Replace with a data::Load() call or similar for a real application.
arma::mat dataset(10, 1000, arma::fill::randu); // 1000 points.
arma::Row<size_t> labels =
    arma::randi<arma::Row<size_t>>(1000, arma::distr_param(0, 4));
arma::mat testData(10, 500, arma::fill::randu); // 500 test points.

mlpack::RandomForest rf;            // Step 1: create model.
rf.Train(dataset, labels, 5, 10);   // Step 2: train model.
arma::Row<size_t> predictions;
rf.Classify(testData, predictions); // Step 3: classify points.
// You can also use `ExtraTrees` instead of `RandomForest`!

// Print some information about the test predictions.
std::cout << arma::accu(predictions == 3) << " test points classified as class "
    << "3." << std::endl;

More examples...

Quick links:

• Constructors: create RandomForest objects.
• Train(): train model.
• Classify(): classify with a trained model.
• Other functionality for loading, saving, and inspecting.
• Examples of simple usage and links to detailed example projects.
• Template parameters for custom behavior.

See also:

• DecisionTree
• DecisionTreeRegressor
• mlpack classifiers
• Random forest on Wikipedia
• Decision tree on Wikipedia
• Leo Breiman's Random Forests page

Constructors

• rf = RandomForest()
  • Initialize the random forest without training.
  • You will need to call Train() later to train the tree before calling Classify().

---

• rf = RandomForest(data, labels, numClasses, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0)
• rf = RandomForest(data, labels, numClasses, weights, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0)
  • Train on numerical-only data (optionally with instance weights).

---

• rf = RandomForest(data, info, labels, numClasses, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0)
• rf = RandomForest(data, info, labels, numClasses, weights, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0)
  • Train on mixed categorical data (optionally with instance weights).

---

Constructor Parameters:

name	type	description	default
data	arma::mat	Column-major training matrix.	(N/A)
info	data::DatasetInfo	Dataset information, specifying type information for each dimension.	(N/A)
labels	arma::Row<size_t>	Training labels, between 0 and numClasses - 1 (inclusive). Should have length data.n_cols.	(N/A)
numClasses	size_t	Number of classes in the dataset.	(N/A)
weights	arma::rowvec	Instance weights for each training point. Should have length data.n_cols.	(N/A)
numTrees	size_t	Number of trees to train in the random forest.	20
minLeafSize	size_t	Minimum number of points in each leaf node of each decision tree.	1
minGainSplit	double	Minimum gain for a node to split in each decision tree.	1e-7
maxDepth	size_t	Maximum depth for each decision tree. (0 means no limit.)	0
warmStart	bool	(Only available in Train().) If true, training adds numTrees trees to the random forest. If false, an entirely new random forest will be created.	false

• If OpenMP is enabled, one thread will be used to train each of the numTrees trees in the random forest. The computational effort involved with training a random forest increases linearly with the number of trees.
• The default minLeafSize is 1, unlike DecisionTree. This is because random forests are less susceptible to overfitting due to their ensembled nature.
• Note that the default minLeafSize of 1 will make large decision trees, and so if a smaller-sized model is desired, this value should be increased (at the potential cost of accuracy).
• minGainSplit can also be increased if a smaller-sized model is desired.

Note: different types can be used for data and weights (e.g., arma::fmat, arma::sp_mat). However, the element type of data and weights must match; for example, if data has type arma::fmat, then weights must have type arma::frowvec.

Training

If training is not done as part of the constructor call, it can be done with one of the following versions of the Train() member function:

• rf.Train(data, labels, numClasses, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0, warmStart=false)
• rf.Train(data, labels, numClasses, weights, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0, warmStart=false)
  • Train on numerical-only data (optionally with instance weights).
  • Returns a double with the average gain of each tree in the random forest. By default, this is the Gini gain, unless a different FitnessFunction template parameter is specified.

---

• rf.Train(data, info, labels, numClasses, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0, warmStart=false)
• rf.Train(data, info, labels, numClasses, weights, numTrees=20, minLeafSize=1, minGainSplit=1e-7, maxDepth=0, warmStart=false)
  • Train on mixed categorical data (optionally with instance weights).

---

Types of each argument are the same as in the table for constructors above.

Notes:

• The warmStart option, which allows incremental training (i.e. additional training on top of an existing model) is of type bool and defaults to false. This option is not available in the constructors.

• Train() returns a double with the average gain of each tree in the random forest. By default, this is the Gini gain, unless a different FitnessFunction template parameter is specified.

Classification

Once a RandomForest is trained, the Classify() member function can be used to make class predictions for new data.

• size_t predictedClass = rf.Classify(point)
  • (Single-point)
  • Classify a single point, returning the predicted class.

---

• rf.Classify(point, prediction, probabilitiesVec)
  • (Single-point)
  • Classify a single point and compute class probabilities.
  • The predicted class is stored in prediction.
  • The probability of class i can be accessed with probabilitiesVec[i].

---

• rf.Classify(data, predictions)
  • (Multi-point)
  • Classify a set of points.
  • The prediction for data point i can be accessed with predictions[i].

---

• rf.Classify(data, predictions, probabilities)
  • (Multi-point)
  • Classify a set of points and compute class probabilities for each point.
  • The prediction for data point i can be accessed with predictions[i].
  • The probability of class j for data point i can be accessed with probabilities(j, i).

---

Classification Parameters:

usage	name	type	description
single-point	point	arma::vec	Single point for classification.
single-point	prediction	size_t&	size_t to store class prediction into.
single-point	probabilitiesVec	arma::vec&	arma::vec& to store class probabilities into. Will be set to length numClasses.
multi-point	data	arma::mat	Set of column-major points for classification.
multi-point	predictions	arma::Row<size_t>&	Vector of size_ts to store class prediction into. Will be set to length data.n_cols.
multi-point	probabilities	arma::mat&	Matrix to store class probabilities into (number of rows will be equal to number of classes, number of columns will be equal to data.n_cols).

Note: different types can be used for data and point (e.g. arma::fmat, arma::sp_mat, arma::sp_vec, etc.). However, the element type that is used should be the same type that was used for training.

Other Functionality

• A RandomForest can be serialized with data::Save() and data::Load().

• rf.NumTrees() will return a size_t indicating the number of trees in the random forest.

• rf.Tree(i) will return a DecisionTree object representing the ith decision tree in the random forest.

For complete functionality, the source code can be consulted. Each method is fully documented.

Simple Examples

See also the simple usage example for a trivial use of RandomForest.

---

Train a random forest incrementally on random mixed categorical data and save it to disk:

// Load a categorical dataset.
arma::mat dataset;
mlpack::data::DatasetInfo info;
// See https://datasets.mlpack.org/covertype.train.arff.
mlpack::data::Load("covertype.train.arff", dataset, info, true);

arma::Row<size_t> labels;
// See https://datasets.mlpack.org/covertype.train.labels.csv.
mlpack::data::Load("covertype.train.labels.csv", labels, true);

// Create the random forest.
mlpack::RandomForest rf;
// Train 10 trees on the given dataset, with a minimum leaf size of 3.
rf.Train(dataset, info, labels, 7 /* classes */, 10 /* trees */,
         3 /* minimum leaf size */);

// Now load categorical test data.
arma::mat testDataset;
// See https://datasets.mlpack.org/covertype.test.arff.
mlpack::data::Load("covertype.test.arff", testDataset, info, true);

arma::Row<size_t> testLabels;
// See https://datasets.mlpack.org/covertype.test.labels.csv.
mlpack::data::Load("covertype.test.labels.csv", testLabels, true);

// Compute test set accuracy.
arma::Row<size_t> testPredictions;
rf.Classify(testDataset, testPredictions);
double accuracy = 100.0 * ((double) arma::accu(testPredictions == testLabels)) /
    testLabels.n_elem;
std::cout << "After training 10 trees, test set accuracy is " << accuracy
    << "%." << std::endl;

// Now train another 10 trees and compute the test accuracy.
rf.Train(dataset, info, labels, 7 /* classes */, 10 /* trees */,
         3 /* minimum leaf size */, 0.0 /* minimum split gain */,
         0 /* maximum depth (unlimited) */, true /* incremental training */);

rf.Classify(testDataset, testPredictions);
accuracy = 100.0 * ((double) arma::accu(testPredictions == testLabels)) /
    testLabels.n_elem;
std::cout << "After training 20 trees, test set accuracy is " << accuracy
    << "%." << std::endl;

// Save the random forest to disk.
mlpack::data::Save("rf.bin", "rf", rf);

---

Load a random forest and print some information about it.

mlpack::RandomForest rf;
// This call assumes a random forest called "rf" has already been saved to
// `rf.bin` with `data::Save()`.
mlpack::data::Load("rf.bin", "rf", rf, true);

std::cout << "The random forest in 'rf.bin' contains " << rf.NumTrees()
    << " trees." << std::endl;
if (rf.NumTrees() > 0)
{
  std::cout << "The first tree's root node has " << rf.Tree(0).NumChildren()
      << " children." << std::endl;
}

---

Train a random forest on categorical data, and compare its performance with the performance of each individual tree:

// Load a categorical dataset (training and test sets).
arma::mat dataset, testDataset;
mlpack::data::DatasetInfo info;
arma::Row<size_t> labels, testLabels;

// See the following files:
//  * https://datasets.mlpack.org/covertype.train.arff
//  * https://datasets.mlpack.org/covertype.train.labels.csv
//  * https://datasets.mlpack.org/covertype.test.arff
//  * https://datasets.mlpack.org/covertype.test.labels.csv
mlpack::data::Load("covertype.train.arff", dataset, info, true);
mlpack::data::Load("covertype.train.labels.csv", labels, true);
mlpack::data::Load("covertype.test.arff", testDataset, info, true);
mlpack::data::Load("covertype.test.labels.csv", testLabels, true);

// Create the random forest.
mlpack::RandomForest rf;
// Train 20 trees on the given dataset, with a minimum leaf size of 5.
rf.Train(dataset, info, labels, 7 /* classes */, 20 /* trees */,
         5 /* minimum leaf size */);

// Compute test set accuracy for each tree.
arma::Row<size_t> testPredictions;
for (size_t i = 0; i < rf.NumTrees(); ++i)
{
  rf.Tree(i).Classify(testDataset, testPredictions);
  const double accuracy = 100.0 *
      ((double) arma::accu(testPredictions == testLabels)) / testLabels.n_elem;
  std::cout << "Tree " << i << " has test accuracy " << accuracy << "%."
      << std::endl;
}

// Now compute accuracy using the whole forest.
rf.Classify(testDataset, testPredictions);
const double accuracy = 100.0 *
    ((double) arma::accu(testPredictions == testLabels)) / testLabels.n_elem;
std::cout << "The whole forest has test accuracy " << accuracy << "%."
    << std::endl;

---

Train an ExtraTrees model on random numeric data.

// 1000 random points in 10 dimensions.
arma::mat dataset(10, 1000, arma::fill::randu);
// Random labels for each point, totaling 5 classes.
arma::Row<size_t> labels =
    arma::randi<arma::Row<size_t>>(1000, arma::distr_param(0, 4));

// Train in the constructor, using 10 trees in the forest.
// Note that `ExtraTrees` has exactly the same API as `RandomForest`.
mlpack::ExtraTrees<> rf(dataset, labels, 5, 10);

// Create a single test point.
arma::vec testPoint(10, arma::fill::randu);

size_t prediction;
arma::vec probabilities;
rf.Classify(testPoint, prediction, probabilities);
std::cout << "Test point predicted to be class " << prediction << "."
    << std::endl;
std::cout << "Probabilities of each class: " << probabilities.t();

---

See also the following fully-working examples:

• Rainfall prediction with RandomForest
• Forest cover type prediction with RandomForest

Advanced Functionality: Template Parameters

Using different element types.

RandomForest's constructors, Train(), and Predict() functions support any data type, so long as it supports the Armadillo matrix API. So, for instance, learning can be done on single-precision floating-point data:

// 1000 random points in 10 dimensions.
arma::fmat dataset(10, 1000, arma::fill::randu);
// Random labels for each point, totaling 5 classes.
arma::Row<size_t> labels =
    arma::randi<arma::Row<size_t>>(1000, arma::distr_param(0, 4));

// Train in the constructor.
mlpack::RandomForest rf(dataset, labels, 5);

// Create test data (500 points).
arma::fmat testDataset(10, 500, arma::fill::randu);
arma::Row<size_t> predictions;
rf.Classify(testDataset, predictions);
// Now `predictions` holds predictions for the test dataset.

// Print some information about the test predictions.
std::cout << arma::accu(predictions == 0) << " test points classified as class "
    << "0." << std::endl;

---

Fully custom behavior.

mlpack provides a few variants of the random forest classifier, using the template parameters of the RandomForest class. The following types can be used as drop-in replacements throughout this documentation page:

• RandomForest

  • This is an implementation of Breiman's seminal random forest algorithm (website, paper pdf).
  • The DecisionTree class is used for each individual decision tree.
  • When training each individual decision tree, bootstrapping is used to compute the samples given to each tree for training.

• ExtraTrees

  • This is an implementation of the Extremely Randomized Trees algorithm (paper pdf).
  • When training an ExtraTrees model, each individual decision tree chooses splits for numeric data randomly.
  • Training an ExtraTrees model is generally much faster than RandomForest, but the accuracy of the ExtraTrees model will be lower.
  • To use ExtraTrees, simply replace RandomForest with ExtraTrees in the documentation below.

---

Fully custom classes can also be used to control the behavior of the RandomForest class. The full signature of the class is as follows:

RandomForest<FitnessFunction,
             DimensionSelectionType,
             NumericSplitType,
             CategoricalSplitType,
             UseBootstrap>

• FitnessFunction: the measure of goodness to use when deciding on tree splits
• DimensionSelectionType: the strategy used for proposing dimensions to attempt to split on
• NumericSplitType: the strategy used for finding splits on numeric data dimensions
• CategoricalSplitType: the strategy used for finding splits on categorical data dimensions
• UseBootstrap: a boolean indicating whether or not to use a bootstrap sample when training each tree in the forest

Note that the first four of these template parameters are exactly the same as the template parameters for the DecisionTree class.

Below, details are given for the requirements of each of these template types.

---

FitnessFunction

• Specifies the fitness function to use when learning a decision tree.
• The GiniGain (default) and InformationGain classes are available for drop-in usage.
• A custom class must implement three functions:

// You can use this as a starting point for implementation.
class CustomFitnessFunction
{
  // Return the range (difference between maximum and minimum gain values).
  double Range(const size_t numClasses);

  // Compute the gain for the given vector of labels, where `labels[i]` has an
  // associated instance weight `weights[i]`.
  //
  // `RowType` and `WeightVecType` will be vector types following the Armadillo
  // API.  If `UseWeights` is `false`, then the `weights` vector should be
  // ignored (e.g. the labels are not weighted).
  template<bool UseWeights, typename RowType, typename WeightVecType>
  double Evaluate(const RowType& labels,
                  const size_t numClasses,
                  const WeightVecType& weights);

  // Compute the gain for the given counted set of labels, where `counts[i]`
  // contains the number of points with label `i`.  There are `totalCount`
  // labels total, and `counts` has length `numClasses`.
  //
  // `UseWeights` is ignored, and `CountType` will be an integral type (e.g.
  // `size_t`).
  template<bool UseWeights, typename CountType>
  double EvaluatePtr(const CountType* counts,
                     const size_t numClasses,
                     const CountType totalCount);
};

---

DimensionSelectionType

• When splitting a tree in the forest, DimensionSelectionType proposes possible dimensions to try splitting on.
• MultipleRandomDimensionSelect (default) is available for drop-in usage and proposes a different random subset of dimensions at each decision tree node.
  • By default each random subset is of size sqrt(d) where d is the number of dimensions in the data.
  • If constructed as MultipleRandomDimensionSelect(n) and passed to the constructor of RandomForest or the Train() function, each random subset will be of size n.
• Each RandomForest constructor and each version of the Train() function optionally accept an instantiated DimensionSelectionType object as the very last parameter (after maxDepth in the constructor, or warmStart in Train()), in case some internal state in the dimension selection mechanism is required.
• A custom class must implement three simple functions:

class CustomDimensionSelect
{
 public:
  // Get the first dimension to try.
  // This should return a value between `0` and `data.n_rows`.
  size_t Begin();

  // Get the next dimension to try.  Note that internal state can be used to
  // track which candidate dimension is currently being looked at.
  // This should return a value between `0` and `data.n_rows`.
  size_t Next();

  // Get a value indicating that all dimensions have been tried.
  size_t End() const;

  // The usage pattern of `DimensionSelectionType` by `DecisionTree` is as
  // follows, assuming that `dim` is an instantiated `DimensionSelectionType`
  // object:
  //
  // for (size_t dim = dim.Begin(); dim != dim.End(); dim = dim.Next())
  // {
  //   // ... try to split on dimension `dim` ...
  // }
};

---

NumericSplitType

• Specifies the strategy to be used during training when splitting a numeric feature.
• The BestBinaryNumericSplit (default) class is available for drop-in usage and finds the best binary (two-way) split among all possible binary splits.
• The RandomBinaryNumericSplit class is available for drop-in usage and will select a split randomly between the minimum and maximum values of a dimension. It is very efficient but does not yield splits that maximize the gain. (Used by the ExtraTrees variant.)
• A custom class must take a FitnessFunction as a template parameter, implement three functions, and have an internal structure AuxiliarySplitInfo that is used at classification time:

template<typename FitnessFunction>
class CustomNumericSplit
{
 public:
  // If a split with better resulting gain than `bestGain` is found, then
  // information about the new, better split should be stored in `splitInfo` and
  // `aux`.  Specifically, a split is better than `bestGain` if the sum of the
  // gains that the children will have (call this `sumChildrenGains`) is
  // sufficiently better than the gain of the unsplit node (call this
  // `unsplitGain`):
  //
  //    split if `sumChildrenGains - unsplitGain > bestGain`, and
  //             `sumChildrenGains - unsplitGain > minGainSplit`, and
  //             each child will have at least `minLeafSize` points
  //
  // The new best split value should be returned (or anything greater than or
  // equal to `bestGain` if no better split is found).
  //
  // If a new best split is found, then `splitInfo` and `aux` should be
  // populated with the information that will be needed for
  // `CalculateDirection()` to successfully choose the child for a given point.
  // `splitInfo` should be set to a vector of length 1.  The format of `aux` is
  // arbitrary and is detailed more below.
  //
  // If `UseWeights` is false, the vector `weights` should be ignored.
  // Otherwise, they are instance weighs for each value in `data` (one dimension
  // of the input data).
  template<bool UseWeights, typename VecType, typename WeightVecType>
  double SplitIfBetter(const double bestGain,
                       const VecType& data,
                       const arma::Row<size_t>& labels,
                       const size_t numClasses,
                       const WeightVecType& weights,
                       const size_t minLeafSize,
                       const double minGainSplit,
                       arma::vec& splitInfo,
                       AuxiliarySplitInfo& aux);

  // Return the number of children for a given split (stored as the single
  // element from `splitInfo` and auxiliary data `aux` in `SplitIfBetter()`).
  size_t NumChildren(const double& splitInfo,
                     const AuxiliarySplitInfo& aux);

  // Given a point with value `point`, and split information `splitInfo` and
  // `aux`, return the index of the child that corresponds to the point.  So,
  // e.g., if the split type was a binary split on the value `splitInfo`, you
  // might return `0` if `point < splitInfo`, and `1` otherwise.
  template<typename ElemType>
  static size_t CalculateDirection(
      const ElemType& point,
      const double& splitInfo,
      const AuxiliarySplitInfo& /* aux */);

  // This class can hold any extra data that is necessary to encode a split.  It
  // should only be non-empty if a single `double` value cannot be used to hold
  // the information corresponding to a split.
  class AuxiliarySplitInfo { };
};

---

CategoricalSplitType

• Specifies the strategy to be used during training when splitting a categorical feature.
• The AllCategoricalSplit (default) is available for drop-in usage and splits all categories into their own node.
• A custom class must take a FitnessFunction as a template parameter, implement three functions, and have an internal structure AuxiliarySplitInfo that is used at classification time:

template<typename FitnessFunction>
class CustomCategoricalSplit
{
 public:
  // If a split with better resulting gain than `bestGain` is found, then
  // information about the new, better split should be stored in `splitInfo` and
  // `aux`.  Specifically, a split is better than `bestGain` if the sum of the
  // gains that the children will have (call this `sumChildrenGains`) is
  // sufficiently better than the gain of the unsplit node (call this
  // `unsplitGain`):
  //
  //    split if `sumChildrenGains - unsplitGain > bestGain`, and
  //             `sumChildrenGains - unsplitGain > minGainSplit`, and
  //             each child will have at least `minLeafSize` points
  //
  // The new best split value should be returned (or anything greater than or
  // equal to `bestGain` if no better split is found).
  //
  // If a new best split is found, then `splitInfo` and `aux` should be
  // populated with the information that will be needed for
  // `CalculateDirection()` to successfully choose the child for a given point.
  // `splitInfo` should be set to a vector of length 1.  The format of `aux` is
  // arbitrary and is detailed more below.
  //
  // If `UseWeights` is false, the vector `weights` should be ignored.
  // Otherwise, they are instance weighs for each value in `data` (one
  // categorical dimension of the input data, which takes values between `0` and
  // `numCategories - 1`).
  template<bool UseWeights, typename VecType, typename LabelsType,
           typename WeightVecType>
  static double SplitIfBetter(
      const double bestGain,
      const VecType& data,
      const size_t numCategories,
      const LabelsType& labels,
      const size_t numClasses,
      const WeightVecType& weights,
      const size_t minLeafSize,
      const double minGainSplit,
      arma::vec& splitInfo,
      AuxiliarySplitInfo& aux);

  // Return the number of children for a given split (stored as the single
  // element from `splitInfo` and auxiliary data `aux` in `SplitIfBetter()`).
  size_t NumChildren(const double& splitInfo,
                     const AuxiliarySplitInfo& aux);

  // Given a point with (categorical) value `point`, and split information
  // `splitInfo` and `aux`, return the index of the child that corresponds to
  // the point.  So, e.g., for `AllCategoricalSplit`, which splits a categorical
  // dimension into one child for each category, this simply returns `point`.
  template<typename ElemType>
  static size_t CalculateDirection(
      const ElemType& point,
      const double& splitInfo,
      const AuxiliarySplitInfo& /* aux */);

  // This class can hold any extra data that is necessary to encode a split.  It
  // should only be non-empty if a single `double` value cannot be used to hold
  // the information corresponding to a split.
  class AuxiliarySplitInfo { };
};

---

UseBootstrap

• A bool value that indicates whether or not a bootstrap sample of the dataset should be used for the training of each individual decision tree in the random forest.
• If true (default), a different bootstrap sample of the same size as the dataset will be used to train each decision tree.
• If false (default for the ExtraTrees variant), the full dataset will be used to train each decision tree.