RegressionTree

Regression tree

Description

A decision tree with binary splits for regression. An object of class RegressionTree can predict responses for new data with the predict method. The object contains the data used for training, so can compute resubstitution predictions using resubPredict.

Creation

Create a RegressionTree object by using fitrtree.

Properties

expand all

`BinEdges` — Bin edges for numeric predictors
cell array of p numeric vectors

This property is read-only.

Bin edges for numeric predictors, specified as a cell array of p numeric vectors, where p is the number of predictors. Each vector includes the bin edges for a numeric predictor. The element in the cell array for a categorical predictor is empty because the software does not bin categorical predictors.

The software bins numeric predictors only if you specify the 'NumBins' name-value argument as a positive integer scalar when training a model with tree learners. The BinEdges property is empty if the 'NumBins' value is empty (default).

You can reproduce the binned predictor data Xbinned by using the BinEdges property of the trained model mdl.

X = mdl.X; % Predictor data
Xbinned = zeros(size(X));
edges = mdl.BinEdges;
% Find indices of binned predictors.
idxNumeric = find(~cellfun(@isempty,edges));
if iscolumn(idxNumeric)
    idxNumeric = idxNumeric';
end
for j = idxNumeric 
    x = X(:,j);
    % Convert x to array if x is a table.
    if istable(x) 
        x = table2array(x);
    end
    % Group x into bins by using the discretize function.
    xbinned = discretize(x,[-inf; edges{j}; inf]); 
    Xbinned(:,j) = xbinned;
end

Xbinned contains the bin indices, ranging from 1 to the number of bins, for numeric predictors. Xbinned values are 0 for categorical predictors. If X contains NaNs, then the corresponding Xbinned values are NaNs.

`CategoricalPredictors` — Indices of categorical predictors
vector of positive integers | `[]`

This property is read-only.

Categorical predictor indices, specified as a vector of positive integers. CategoricalPredictors contains index values indicating that the corresponding predictors are categorical. The index values are between 1 and p, where p is the number of predictors used to train the model. If none of the predictors are categorical, then this property is empty ([]).

Data Types: single | double

`CategoricalSplit` — Categorical splits
`n`-by-2 cell array

This property is read-only.

Categorical splits, returned as an n-by-2 cell array, where n is the number of categorical splits in tree. Each row in CategoricalSplit gives left and right values for a categorical split. For each branch node with categorical split j based on a categorical predictor variable z, the left child is chosen if z is in CategoricalSplit(j,1) and the right child is chosen if z is in CategoricalSplit(j,2). The splits are in the same order as nodes of the tree. Nodes for these splits can be found by running cuttype and selecting 'categorical' cuts from top to bottom.

Data Types: cell

`Children` — Numbers of the child nodes for each node
`n`-by-2 array

This property is read-only.

Numbers of the child nodes for each node in the tree, returned as an n-by-2 array, where n is the number of nodes. Leaf nodes have child node 0.

Data Types: double

`CutCategories` — Categories used at branches
`n`-by-2 cell array

This property is read-only.

Categories used at branches in tree, returned as an n-by-2 cell array, where n is the number of nodes. For each branch node i based on a categorical predictor variable X, the left child is chosen if X is among the categories listed in CutCategories{i,1}, and the right child is chosen if X is among those listed in CutCategories{i,2}. Both columns of CutCategories are empty for branch nodes based on continuous predictors and for leaf nodes.

CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories.

Data Types: cell

`CutPoint` — Values used as cut points
`n`-element vector

This property is read-only.

Values used as cut points in tree, returned as an n-element vector, where n is the number of nodes. For each branch node i based on a continuous predictor variable X, the left child is chosen if X<CutPoint(i) and the right child is chosen if X>=CutPoint(i). CutPoint is NaN for branch nodes based on categorical predictors and for leaf nodes.

CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories.

Data Types: double

`CutPredictor` — Names of the variables used for branching in each node
cell array

This property is read-only.

Names of the variables used for branching in each node in tree, returned as an n-element cell array, where n is the number of nodes. These variables are sometimes known as cut variables. For leaf nodes, CutPredictor contains an empty character vector.

CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories.

Data Types: cell

`CutPredictorIndex` — Indices of variables used for branching in each node
`n`-element array

This property is read-only.

Indices of variables used for branching in each node in tree, returned as an n-element array, where n is the number of nodes. For more information, see CutPredictor.

Data Types: double

`CutType` — Type of cut at each node
`n`-element cell array

This property is read-only.

Type of cut at each node in tree, returned as an n-element cell array, where n is the number of nodes. For each node i, CutType{i} is:

'continuous' — If the cut is defined in the form X < v for a variable X and cut point v.
'categorical' — If the cut is defined by whether a variable X takes a value in a set of categories.
'' — If i is a leaf node.

CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories.

Data Types: cell

`ExpandedPredictorNames` — Expanded predictor names
cell array of character vectors

This property is read-only.

Expanded predictor names, returned as a cell array of character vectors.

If the model uses encoding for categorical variables, then ExpandedPredictorNames includes the names that describe the expanded variables. Otherwise, ExpandedPredictorNames is the same as PredictorNames.

Data Types: cell

`HyperparameterOptimizationResults` — Description of cross-validation optimization of hyperparameters
`BayesianOptimization` object | table of hyperparameters and associated values

This property is read-only.

Description of the cross-validation optimization of hyperparameters, returned as a BayesianOptimization object or a table of hyperparameters and associated values. Nonempty when the OptimizeHyperparameters name-value pair is nonempty at creation. Value depends on the setting of the HyperparameterOptimizationOptions name-value pair at creation:

'bayesopt' (default) — Object of class BayesianOptimization
'gridsearch' or 'randomsearch' — Table of hyperparameters used, observed objective function values (cross-validation loss), and rank of observations from lowest (best) to highest (worst)

`IsBranchNode` — Indicator of branch nodes
logical vector

This property is read-only.

Indicator of branch nodes, returned as an n-element logical vector that is true for each branch node and false for each leaf node of tree.

Data Types: logical

`ModelParameters` — Parameters used in training `tree`
`TreeParams` object

This property is read-only.

Parameters used in training tree, returned as a TreeParams object. To display all parameter values, enter tree.ModelParameters. To access a particular parameter, use dot notation.

`NodeError` — Mean squared error for each node
`n`-element vector

This property is read-only.

Mean squared error for each node in tree, returned as an n-element vector, where n is the number of nodes in the tree.

Data Types: double

`NodeMean` — Mean observation values for each node
`n`-element vector

This property is read-only.

Mean observation values for each node in tree, returned as an n-element vector, where n is the number of nodes in the tree. Every element in NodeMean is the average of the true Y values over all observations in the node.

Data Types: double

`NodeProbability` — Proportion of observations in original data that satisfy the conditions for the node
`n`-element vector

This property is read-only.

Proportion of observations in original data that satisfy the conditions for each node in tree, returned as an n-element vector, where n is the number of nodes in the tree.

Data Types: double

`NodeRisk` — Risk of each node
`n`-element vector

This property is read-only.

Risk of each node in tree, returned as an n-element vector, where n is the number of nodes in the tree. The risk for each node is the node error weighted by the node probability.

Data Types: double

`NodeSize` — Size of nodes
`n`-element vector

This property is read-only.

Size of the nodes in tree, returned as an n-element vector, where n is the number of nodes in the tree. The size of a node is the number of observations from the data used to create the tree that satisfy the conditions for the node.

Data Types: double

`NumNodes` — Number of nodes
positive integer

This property is read-only.

The number of nodes in tree, returned as a positive integer.

Data Types: double

`NumObservations` — Number of observations in the training data
positive integer

This property is read-only.

Number of observations in the training data, returned as a positive integer. NumObservations can be less than the number of rows of input data when there are missing values in the input data or response data.

Data Types: double

`Parent` — Number of parents of nodes
`n`-element vector

This property is read-only.

Number of parents of each node in tree, returned as an n-element integer vector, where n is the number of nodes in the tree. The parent of the root node is 0.

Data Types: double

`PredictorNames` — Predictor names
cell array of character vectors

This property is read-only.

Predictor names, specified as a cell array of character vectors. The order of the entries in PredictorNames is the same as in the training data.

Data Types: cell

`PruneAlpha` — Alpha values for pruning the tree
real vector

Alpha values for pruning the tree, returned as a real vector with one element per pruning level. If the pruning level ranges from 0 to M, then PruneAlpha has M + 1 elements sorted in ascending order. PruneAlpha(1) is for pruning level 0 (no pruning), PruneAlpha(2) is for pruning level 1, and so on.

For the meaning of the ɑ values, see How Decision Trees Create a Pruning Sequence.

Data Types: double

`PruneList` — Pruning levels of each node in tree
integer vector

Pruning levels of each node in the tree, returned as an integer vector with NumNodes elements. The pruning levels range from 0 (no pruning) to M, where M is the distance between the deepest leaf and the root node.

For details, see Pruning.

Data Types: double

`ResponseName` — Name of the response variable
character vector

This property is read-only.

Name of the response variable, returned as a character vector.

Data Types: char

`ResponseTransform` — Function for transforming responses
`'none'` (default) | function handle

Function for transforming the raw response values (mean squared error), specified as a function handle or 'none'. The default 'none' means no transformation; equivalently, 'none' means @(x)x. A function handle must accept a matrix of response values and return a matrix of the same size.

Add or change a ResponseTransform function using dot notation:

tree.ResponseTransform = @function

Data Types: char | function_handle

`RowsUsed` — Rows of the original predictor data `X` used for fitting
logical vector

This property is read-only.

Rows of the original predictor data X used for fitting, returned as an n-element logical vector, where n is the number of rows of X. If the software uses all rows of X for constructing the object, then RowsUsed is an empty array ([]).

Data Types: logical

`SurrogateCutCategories` — Categories used for surrogate splits
`n`-element cell array

This property is read-only.

Categories used for surrogate splits, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogateCutCategories{k} is a cell array. The length of SurrogateCutCategories{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogateCutCategories{k} is either an empty character vector for a continuous surrogate predictor, or is a two-element cell array with categories for a categorical surrogate predictor. The first element of this two-element cell array lists categories assigned to the left child by this surrogate split and the second element of this two-element cell array lists categories assigned to the right child by this surrogate split. The order of the surrogate split variables at each node is matched to the order of variables in SurrogateCutVar. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutCategories contains an empty cell.

Data Types: cell

`SurrogateCutFlip` — Numeric cut assignments used for surrogate splits
`n`-element cell array

This property is read-only.

Numeric cut assignments used for surrogate splits in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogateCutFlip{k} is a numeric vector. The length of SurrogateCutFlip{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogateCutFlip{k} is either zero for a categorical surrogate predictor, or a numeric cut assignment for a continuous surrogate predictor. The numeric cut assignment can be either –1 or +1. For every surrogate split with a numeric cut C based on a continuous predictor variable Z, the left child is chosen if Z<C and the cut assignment for this surrogate split is +1, or if Z≥C and the cut assignment for this surrogate split is –1. Similarly, the right child is chosen if Z≥C and the cut assignment for this surrogate split is +1, or if Z<C and the cut assignment for this surrogate split is –1. The order of the surrogate split variables at each node is matched to the order of variables in SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutFlip contains an empty array.

Data Types: cell

`SurrogateCutPoint` — Numeric values used for surrogate splits
`n`-element cell array

This property is read-only.

Numeric values used for surrogate splits in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogateCutPoint{k} is a numeric vector. The length of SurrogateCutPoint{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogateCutPoint{k} is either NaN for a categorical surrogate predictor, or a numeric cut for a continuous surrogate predictor. For every surrogate split with a numeric cut C based on a continuous predictor variable Z, the left child is chosen if Z<C and SurrogateCutFlip for this surrogate split is +1, or if Z≥C and SurrogateCutFlip for this surrogate split is –1. Similarly, the right child is chosen if Z≥C and SurrogateCutFlip for this surrogate split is +1, or if Z<C and SurrogateCutFlip for this surrogate split is –1. The order of the surrogate split variables at each node is matched to the order of variables returned by SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutPoint contains an empty cell.

Data Types: cell

`SurrogateCutPredictor` — Names of variables used for surrogate splits in each node
`n`-element cell array

This property is read-only.

Names of the variables used for surrogate splits in each node in tree, returned as an n-element cell array, where n is the number of nodes in tree. Every element of SurrogateCutPredictor is a cell array with the names of the surrogate split variables at this node. The variables are sorted by the predictive measure of association with the optimal predictor in the descending order, and only variables with the positive predictive measure are included. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutPredictor contains an empty cell.

Data Types: cell

`SurrogateCutType` — Types of surrogate splits at each node
`n`-element cell array

This property is read-only.

Types of surrogate splits at each node in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogateCutType{k} is a cell array with the types of the surrogate split variables at this node. The variables are sorted by the predictive measure of association with the optimal predictor in the descending order, and only variables with the positive predictive measure are included. The order of the surrogate split variables at each node is matched to the order of variables in SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutType contains an empty cell. A surrogate split type can be either 'continuous' if the cut is defined in the form Z<V for a variable Z and cut point V or 'categorical' if the cut is defined by whether Z takes a value in a set of categories.

Data Types: cell

`SurrogatePredictorAssociation` — Predictive measures of association for surrogate splits
`n`-element cell array

This property is read-only.

Predictive measures of association for surrogate splits in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogatePredictorAssociation{k} is a numeric vector. The length of SurrogatePredictorAssociation{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogatePredictorAssociation{k} gives the predictive measure of association between the optimal split and this surrogate split. The order of the surrogate split variables at each node is the order of variables in SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogatePredictorAssociation contains an empty cell.

Data Types: cell

`W` — Scaled weights in tree
numeric vector

This property is read-only.

Scaled weights in tree, returned as a numeric vector. W has length n, the number of rows in the training data.

Data Types: double

`X` — Predictor values
real matrix | table

This property is read-only.

Predictor values, returned as a real matrix or table. Each column of X represents one variable (predictor), and each row represents one observation.

Data Types: double | table

`Y` — Response data
numeric column vector

This property is read-only.

Response data, returned as a numeric column vector with the same number of rows as X. Each entry in Y is the response to the data in the corresponding row of X.

Data Types: double

Object Functions

`compact`	Reduce size of regression tree model
`crossval`	Cross-validate machine learning model
`cvloss`	Regression error by cross-validation for regression tree model
`gather`	Gather properties of Statistics and Machine Learning Toolbox object from GPU
`lime`	Local interpretable model-agnostic explanations (LIME)
`loss`	Regression error for regression tree model
`nodeVariableRange`	Retrieve variable range of decision tree node
`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`predict`	Predict responses using regression tree model
`predictorImportance`	Estimates of predictor importance for regression tree
`prune`	Produce sequence of regression subtrees by pruning regression tree
`resubLoss`	Resubstitution loss for regression tree model
`resubPredict`	Predict response of regression tree by resubstitution
`shapley`	Shapley values
`surrogateAssociation`	Mean predictive measure of association for surrogate splits in regression tree
`view`	View regression tree

Examples

collapse all

Construct Regression Tree

Open Live Script

Load the sample data.

load carsmall

Construct a regression tree using the sample data. The response variable is miles per gallon, MPG.

tree = fitrtree([Weight, Cylinders],MPG,...
                'CategoricalPredictors',2,'MinParentSize',20,...
                'PredictorNames',{'W','C'})

tree = 
  RegressionTree
           PredictorNames: {'W'  'C'}
             ResponseName: 'Y'
    CategoricalPredictors: 2
        ResponseTransform: 'none'
          NumObservations: 94

Predict the mileage of 4,000-pound cars with 4, 6, and 8 cylinders.

MPG4Kpred = predict(tree,[4000 4; 4000 6; 4000 8])

MPG4Kpred = 3×1

   19.2778
   19.2778
   14.3889

References

[1] Breiman, L., J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees. Boca Raton, FL: CRC Press, 1984.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The predict and update functions support code generation.
To integrate the prediction of a regression tree model into Simulink^®, you can use the RegressionTree Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB^® Function block with the predict function.
When you train a regression tree model by using fitrtree, the following restrictions apply.
- The value of the ResponseTransform name-value argument cannot be an anonymous function. For fixed-point code generation, the value must be 'none' (default).
- You cannot use surrogate splits; that is, the value of the Surrogate name-value argument must be 'off'.
- Fixed-point code generation and code generation with a coder configurer do not support categorical predictors (logical, categorical, char, string, or cell). You cannot use the CategoricalPredictors name-value argument. To include categorical predictors in a model, preprocess them by using dummyvar before fitting the model.

For more information, see Introduction to Code Generation.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

The following object functions fully support GPU arrays:
The following object functions offer limited support for GPU arrays:
The object functions execute on a GPU if at least one of the following applies:
- The model was fitted with GPU arrays.
- The predictor data that you pass to the object function is a GPU array.
- The response data that you pass to the object function is a GPU array.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2011a

RegressionTree

Description

Creation

Properties

BinEdges — Bin edges for numeric predictors cell array of p numeric vectors

CategoricalPredictors — Indices of categorical predictors vector of positive integers | []

CategoricalSplit — Categorical splits n-by-2 cell array

Children — Numbers of the child nodes for each node n-by-2 array

CutCategories — Categories used at branches n-by-2 cell array

CutPoint — Values used as cut points n-element vector

CutPredictor — Names of the variables used for branching in each node cell array

CutPredictorIndex — Indices of variables used for branching in each node n-element array

CutType — Type of cut at each node n-element cell array

ExpandedPredictorNames — Expanded predictor names cell array of character vectors

HyperparameterOptimizationResults — Description of cross-validation optimization of hyperparameters BayesianOptimization object | table of hyperparameters and associated values

IsBranchNode — Indicator of branch nodes logical vector

ModelParameters — Parameters used in training tree TreeParams object

NodeError — Mean squared error for each node n-element vector

NodeMean — Mean observation values for each node n-element vector

NodeProbability — Proportion of observations in original data that satisfy the conditions for the node n-element vector

NodeRisk — Risk of each node n-element vector

NodeSize — Size of nodes n-element vector

NumNodes — Number of nodes positive integer

NumObservations — Number of observations in the training data positive integer

Parent — Number of parents of nodes n-element vector

PredictorNames — Predictor names cell array of character vectors

PruneAlpha — Alpha values for pruning the tree real vector

PruneList — Pruning levels of each node in tree integer vector

ResponseName — Name of the response variable character vector

ResponseTransform — Function for transforming responses 'none' (default) | function handle

RowsUsed — Rows of the original predictor data X used for fitting logical vector

SurrogateCutCategories — Categories used for surrogate splits n-element cell array

SurrogateCutFlip — Numeric cut assignments used for surrogate splits n-element cell array

SurrogateCutPoint — Numeric values used for surrogate splits n-element cell array

SurrogateCutPredictor — Names of variables used for surrogate splits in each node n-element cell array

SurrogateCutType — Types of surrogate splits at each node n-element cell array

SurrogatePredictorAssociation — Predictive measures of association for surrogate splits n-element cell array

W — Scaled weights in tree numeric vector

X — Predictor values real matrix | table

Y — Response data numeric column vector

Object Functions

Examples

Construct Regression Tree

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Version History

See Also

Topics

`BinEdges` — Bin edges for numeric predictors
cell array of p numeric vectors

`CategoricalPredictors` — Indices of categorical predictors
vector of positive integers | `[]`

`CategoricalSplit` — Categorical splits
`n`-by-2 cell array

`Children` — Numbers of the child nodes for each node
`n`-by-2 array

`CutCategories` — Categories used at branches
`n`-by-2 cell array

`CutPoint` — Values used as cut points
`n`-element vector

`CutPredictor` — Names of the variables used for branching in each node
cell array

`CutPredictorIndex` — Indices of variables used for branching in each node
`n`-element array

`CutType` — Type of cut at each node
`n`-element cell array

`ExpandedPredictorNames` — Expanded predictor names
cell array of character vectors

`HyperparameterOptimizationResults` — Description of cross-validation optimization of hyperparameters
`BayesianOptimization` object | table of hyperparameters and associated values

`IsBranchNode` — Indicator of branch nodes
logical vector

`ModelParameters` — Parameters used in training `tree`
`TreeParams` object

`NodeError` — Mean squared error for each node
`n`-element vector

`NodeMean` — Mean observation values for each node
`n`-element vector

`NodeProbability` — Proportion of observations in original data that satisfy the conditions for the node
`n`-element vector

`NodeRisk` — Risk of each node
`n`-element vector

`NodeSize` — Size of nodes
`n`-element vector

`NumNodes` — Number of nodes
positive integer

`NumObservations` — Number of observations in the training data
positive integer

`Parent` — Number of parents of nodes
`n`-element vector

`PredictorNames` — Predictor names
cell array of character vectors

`PruneAlpha` — Alpha values for pruning the tree
real vector

`PruneList` — Pruning levels of each node in tree
integer vector

`ResponseName` — Name of the response variable
character vector

`ResponseTransform` — Function for transforming responses
`'none'` (default) | function handle

`RowsUsed` — Rows of the original predictor data `X` used for fitting
logical vector

`SurrogateCutCategories` — Categories used for surrogate splits
`n`-element cell array

`SurrogateCutFlip` — Numeric cut assignments used for surrogate splits
`n`-element cell array

`SurrogateCutPoint` — Numeric values used for surrogate splits
`n`-element cell array

`SurrogateCutPredictor` — Names of variables used for surrogate splits in each node
`n`-element cell array

`SurrogateCutType` — Types of surrogate splits at each node
`n`-element cell array

`SurrogatePredictorAssociation` — Predictive measures of association for surrogate splits
`n`-element cell array

`W` — Scaled weights in tree
numeric vector

`X` — Predictor values
real matrix | table

`Y` — Response data
numeric column vector

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.