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DecisionTreeRegressor

The DecisionTreeRegressor class implements a decision tree regressor that supports numerical and categorical features, by default using MSE (minimum squared error) to choose which feature to split on. The class offers several template parameters and runtime options that can be used to control the behavior of the tree.

The DecisionTreeRegressor class is useful for regressions; i.e., predicting continuous values (0.3, 1.2, etc.). For predicting discrete labels (classification), see DecisionTree.

Simple usage example:

Train a decision tree regressor on random numeric data and make predictions on a test set:

// Train a decision tree regressor on random numeric data and make predictions.

// All data and responses are uniform random; this uses 10 dimensional data.
// Replace with a data::Load() call or similar for a real application.
arma::mat dataset(10, 1000, arma::fill::randu); // 1000 points.
arma::rowvec responses = arma::randn<arma::rowvec>(1000);
arma::mat testDataset(10, 500, arma::fill::randu); // 500 test points.

mlpack::DecisionTreeRegressor tree;     // Step 1: create tree.
tree.Train(dataset, responses);         // Step 2: train model.
arma::rowvec predictions;
tree.Predict(testDataset, predictions); // Step 3: use model to predict.

// Print some information about the test predictions.
std::cout << arma::accu(predictions > 0.7) << " test points predicted to have"
    << " responses greater than 0.7." << std::endl;
std::cout << arma::accu(predictions < 0) << " test points predicted to have "
    << "negative responses." << std::endl;

More examples...

Quick links:

See also:

Constructors

  • tree = DecisionTreeRegressor()
    • Initialize tree without training.
    • You will need to call Train() later to train the tree before calling Predict().
  • tree = DecisionTreeRegressor(data, responses, minLeafSize=10, minGainSplit=1e-7, maxDepth=0)
  • tree = DecisionTreeRegressor(data, responses, weights, minLeafSize=10, minGainSplit=1e-7, maxDepth=0)
    • Train on numerical-only data (optionally with instance weights).
  • tree = DecisionTreeRegressor(data, datasetInfo, responses, minLeafSize=10, minGainSplit=1e-7, maxDepth=0)
  • tree = DecisionTreeRegressor(data, datasetInfo, responses, weights, minLeafSize=10, 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)
datasetInfo data::DatasetInfo Dataset information, specifying type information for each dimension. (N/A)
responses arma::rowvec Training responses (e.g. values to predict). Should have length data.n_cols. (N/A)
weights arma::rowvec Weights for each training point. Should have length data.n_cols. (N/A)
numClasses size_t Number of classes in the dataset. (N/A)
minLeafSize size_t Minimum number of points in each leaf node. 10
minGainSplit double Minimum gain for a node to split. 1e-7
maxDepth size_t Maximum depth for the tree. (0 means no limit.) 0
  • Setting minLeafSize too small (e.g. 1) may cause the tree to overfit to its training data, and may create a very large tree. However, setting it too large may cause the tree to be very small and underfit.
  • minGainSplit has similar behavior: if it is too small, the tree may overfit; if too large, it may underfit.

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

Training

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

  • tree.Train(data, responses, minLeafSize=10, minGainSplit=1e-7, maxDepth=0)
  • tree.Train(data, responses, weights, minLeafSize=10, minGainSplit=1e-7, maxDepth=0)
    • Train on numerical-only data (optionally with instance weights).
  • tree.Train(data, datasetInfo, responses)
  • tree.Train(data, datasetInfo, responses, weights)
  • tree.Train(data, datasetInfo, responses, minLeafSize, minGainSplit, maxDepth)
  • tree.Train(data, datasetInfo, responses, weights, minLeafSize, minGainSplit, maxDepth)
    • Train on mixed categorical data (optionally with instance weights).

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

Notes:

  • Training is not incremental. A second call to Train() will retrain the decision tree from scratch.

  • Train() returns a double with the final gain of the tree (the Gini gain, unless a different FitnessFunction template parameter is specified.

Prediction

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

  • double predictedValue = tree.Predict(point)
    • (Single-point)
    • Predict and return the value for a single point.
  • tree.Predict(data, predictions)
    • (Multi-point)
    • Predict and return values for every point in the given matrix data.
    • The predictions for each point are stored in predictions, which is set to length data.n_cols.
    • The prediction for data point i can be accessed with predictions[i].

Prediction Parameters:

usage name type description
single-point point arma::vec Single point for prediction.
multi-point data arma::mat Set of column-major points for prediction.
multi-point predictions arma::rowvec& Vector to store predictions into.

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 DecisionTreeRegressor can be serialized with data::Save() and data::Load().

  • tree.NumChildren() will return a size_t indicating the number of children in the node tree.

  • tree.NumLeaves() will return the total number of leaf nodes that are descendants of the node tree.

  • tree.Child(i) will return a DecisionTreeRegressor object representing the ith child of the node tree.

  • tree.SplitDimension() returns a size_t indicating which dimension the node tree splits on.

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 DecisionTreeRegressor.

Train a decision tree regressor on mixed categorical data.

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

arma::rowvec responses;
// See https://datasets.mlpack.org/telecom_churn.responses.csv.
mlpack::data::Load("telecom_churn.responses.csv", responses, true);

// Split data into training set (80%) and test set (20%).
arma::mat trainData, testData;
arma::rowvec trainResponses, testResponses;
mlpack::data::Split(data, responses, trainData, testData, trainResponses,
    testResponses, 0.2);

// Create the tree.
mlpack::DecisionTreeRegressor tree;
// Train on the given dataset, specifying a minimum gain of 1e-6 and keeping the
// default minimum leaf size.
const double mse = tree.Train(trainData, info, trainResponses,
    10 /* minimum leaf size */, 1e-6 /* minimum gain */);
// Print the MSE of the trained tree.
std::cout << "MSE of trained tree is " << mse << "." << std::endl;

// Compute prediction on the first test point.
const double firstPrediction = tree.Predict(testData.col(0));
std::cout << "Predicted value for first test point is " << firstPrediction
    << "." << std::endl;

// Compute predictions on test data.
arma::rowvec testPredictions;
tree.Predict(testData, testPredictions);

// Compute the average error on the test set.
const double testAverageError = arma::mean(testResponses - testPredictions);
std::cout << "Average error on test set: " << testAverageError << "."
    << std::endl;

Load a tree and print some information about it.

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

std::cout << "Information about the DecisionTreeRegressor in `tree.bin`:"
    << std::endl;
std::cout << " * The root node has " << tree.NumChildren() << " children."
    << std::endl;
std::cout << " * The tree has " << tree.NumLeaves() << " leaves." << std::endl;
if (tree.NumChildren() > 0)
{
  for (size_t i = 0; i < tree.NumChildren(); ++i)
  {
    std::cout << " * Child " << i << " of the root has "
        << tree.Child(i).NumLeaves() << " leaves in its subtree." << std::endl;
  }
}

Advanced Functionality: Template Parameters

Using different element types.

DecisionTreeRegressor'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 responses for each point, with a normal distribution.
arma::frowvec responses = arma::randn<arma::frowvec>(1000);

// Train in the constructor.
mlpack::DecisionTreeRegressor tree(dataset, responses, 5);

// Create test data (500 points).
arma::fmat testDataset(10, 500, arma::fill::randu);
arma::frowvec predictions;
tree.Predict(testDataset, predictions);
// Now `predictions` holds predictions for the test dataset.

// Print some information about the test predictions.
std::cout << arma::accu(predictions > 1) << " test points predicted to have "
    << "value greater than 1." << std::endl;

Fully custom behavior.

The DecisionTreeRegressor class also supports several template parameters, which can be used for custom behavior during learning. The full signature of the class is as follows:

DecisionTreeRegressor<FitnessFunction,
                      NumericSplitType,
                      CategoricalSplitType,
                      DimensionSelectionType,
                      NoRecursion>
  • FitnessFunction: the measure of goodness to use when deciding on tree splits
  • NumericSplitType: the strategy used for finding splits on numeric data dimensions
  • CategoricalSplitType: the strategy used for finding splits on categorical data dimensions
  • DimensionSelectionType: the strategy used for proposing dimensions to attempt to split on
  • NoRecursion: a boolean indicating whether to build a tree or a stump (one level tree)

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 MSEGain (default) and MADGain 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
{
  // Compute the gain for the given vector of values, where `values[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 responses are not weighted).
  //
  // In the version with `begin` and `end` parameters, only the subset between
  // `labels[begin]` and `labels[end]` (inclusive) should be considered.
  template<bool UseWeights, typename RowType, typename WeightVecType>
  double Evaluate(const RowType& labels,
                  const WeightVecType& weights);

  template<bool UseWeights, typename RowType, typename WeightVecType>
  double Evaluate(const RowType& labels,
                  const WeightVecType& weights,
                  const size_t begin,
                  const size_t end);

  // Return the output value for prediction for a leaf node whose training
  // values are made up of the values in the vector `responses` (optionally with
  // associated instance weights `weights`).
  //
  // `ResponsesType` and `WeightsType` will be vector types following the
  // Armadillo API.  If `UseWeights` is `false`, then the `weights` vector
  // should be ignored (e.g. the responses are not weighted).
  template<bool UseWeights, typename ResponsesType, typename WeightsType>
  double OutputLeafValue(const ResponsesType& responses,
                         const WeightsType& weights);
};

Note: this API differs from the FitnessFunction API required for DecisionTree!

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 of RandomForest.)
  • 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:
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 ResponsesType,
      typename WeightVecType>
  double SplitIfBetter(const double bestGain,
                       const VecType& data,
                       const ResponsesType& responses,
                       const WeightVecType& weights,
                       const size_t minLeafSize,
                       const double minGainSplit,
                       arma::vec& splitInfo,
                       AuxiliarySplitInfo& aux,
                       FitnessFunction& function);

  // 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 { };
};

Note: this API differs from the NumericSplitType API required for DecisionTree!

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:
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 ResponsesType,
           typename WeightVecType>
  static double SplitIfBetter(
      const double bestGain,
      const VecType& data,
      const size_t numCategories,
      const ResponsesType& labels,
      const WeightVecType& weights,
      const size_t minLeafSize,
      const double minGainSplit,
      arma::vec& splitInfo,
      AuxiliarySplitInfo& aux,
      FitnessFunction& fitnessFunction);

  // 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 { };
};

Note: this API differs from the CategoricalSplitType API required for DecisionTree!

DimensionSelectionType

  • When splitting a decision tree, DimensionSelectionType proposes possible dimensions to try splitting on.
  • AllDimensionSplit (default) is available for drop-in usage and proposes all dimensions for splits.
  • MultipleRandomDimensionSelect 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 DecisionTree<> or the Train() function, each random subset will be of size n.
  • Each DecisionTreeRegressor constructor and each version of the Train() function optionally accept an instantiated DimensionSelectionType object as the very last parameter (after maxDepth), 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` ...
  // }
};

NoRecursion

  • A bool value that indicates whether a decision tree should be constructed recursively.
  • If true, only the root node will be split (producing a decision stump).
  • If false (default), a full decision tree will be built.