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RegressionTree class

Superclasses: CompactRegressionTree

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.

Construction

Create a RegressionTree object by using fitrtree.

Properties

CategoricalPredictors

Categorical predictor indices, specified as a vector of positive integers. CategoricalPredictors contains index values corresponding to the columns of the predictor data that contain categorical predictors. If none of the predictors are categorical, then this property is empty ([]).

CategoricalSplits

An n-by-2 cell array, where n is the number of categorical splits in tree. Each row in CategoricalSplits 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 CategoricalSplits(j,1) and the right child is chosen if z is in CategoricalSplits(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.

Children

An n-by-2 array containing the numbers of the child nodes for each node in tree, where n is the number of nodes. Leaf nodes have child node 0.

CutCategories

An n-by-2 cell array of the categories used at branches in tree, 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.

CutPoint

An n-element vector of the values used as cut points in tree, 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.

CutType

An n-element cell array indicating the type of cut at each node in tree, 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.

CutPredictor

An n-element cell array of the names of the variables used for branching in each node in tree, 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.

ExpandedPredictorNames

Expanded predictor names, stored 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.

HyperparameterOptimizationResults

Description of the cross-validation optimization of hyperparameters, stored 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

An n-element logical vector ib that is true for each branch node and false for each leaf node of tree.

ModelParameters

Object holding parameters of tree.

NumObservations

Number of observations in the training data, a numeric scalar. NumObservations can be less than the number of rows of input data X when there are missing values in X or response Y.

NodeError

An n-element vector e of the errors of the nodes in tree, where n is the number of nodes. e(i) is the misclassification probability for node i.

NodeMean

An n-element numeric array with mean values in each node of tree, 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.

NodeProbability

An n-element vector p of the probabilities of the nodes in tree, where n is the number of nodes. The probability of a node is computed as the proportion of observations from the original data that satisfy the conditions for the node. This proportion is adjusted for any prior probabilities assigned to each class.

NodeRisk

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

NodeSize

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

NumNodes

The number of nodes n in tree.

Parent

An n-element vector p containing the number of the parent node for each node in tree, where n is the number of nodes. The parent of the root node is 0.

PredictorNames

A cell array of names for the predictor variables, in the order in which they appear in X.

PruneAlpha

Numeric 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.

PruneList

An n-element numeric vector with the pruning levels in each node of tree, where n is the number of nodes. The pruning levels range from 0 (no pruning) to M, where M is the distance between the deepest leaf and the root node.

ResponseName

A character vector that specifies the name of the response variable (Y).

ResponseTransform

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

Add or change a ResponseTransform function using dot notation:

tree.ResponseTransform = @function

RowsUsed

An n-element logical vector indicating which rows of the original predictor data (X) were used in fitting. If the software uses all rows of X, then RowsUsed is an empty array ([]).

SurrogateCutCategories

An n-element cell array of the categories used for surrogate splits in tree, 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 SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutCategories contains an empty cell.

SurrogateCutFlip

An n-element cell array of the numeric cut assignments used for surrogate splits in tree, 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.

SurrogateCutPoint

An n-element cell array of the numeric values used for surrogate splits in tree, 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 ZC 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 SurrCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutPoint contains an empty cell.

SurrogateCutType

An n-element cell array indicating types of surrogate splits at each node in tree, 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.

SurrogateCutPredictor

An n-element cell array of the names of the variables used for surrogate splits in each node in tree, 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.

SurrogatePredictorAssociation

An n-element cell array of the predictive measures of association for surrogate splits in tree, 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.

W

The scaled weights, a vector with length n, the number of rows in X.

X

A matrix of predictor values. Each column of X represents one variable, and each row represents one observation.

Y

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.

Methods

compactCompact regression tree
crossvalCross-validated decision tree
cvlossRegression error by cross validation
pruneProduce sequence of subtrees by pruning
resubLossRegression error by resubstitution
resubPredictPredict resubstitution response of tree

Inherited Methods

lossRegression error
predictPredict responses using regression tree
predictorImportanceEstimates of predictor importance
surrogateAssociationMean predictive measure of association for surrogate splits in decision tree
viewView tree

Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB).

Examples

collapse all

Load the sample data.

load carsmall;

Construct a regression tree using the sample data.

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


  Properties, Methods

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

mileage4K = predict(tree,[4000 4; 4000 6; 4000 8])
mileage4K = 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

Introduced in R2011a