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cvloss

Regression error by cross-validation for regression tree model

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Syntax

E = cvloss(tree)
E = cvloss(tree,Name=Value)
[E,SE,Nleaf,BestLevel] = cvloss(___)

Description

E = cvloss(tree) returns the cross-validated regression error (loss) E for the trained regression tree model tree.

example

E = cvloss(tree,Name=Value) specifies additional options using one or more name-value arguments. For example, you can specify the pruning level, tree size, and number of cross-validation samples.

example

[E,SE,Nleaf,BestLevel] = cvloss(___) also returns the standard error of E, the number of leaf nodes of tree, and the optimal pruning level for tree, using any of the input argument combinations in the previous syntaxes.

example

Examples

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Open Live Script

Compute the cross-validation error for a default regression tree.

Load the carsmall data set. Consider Displacement, Horsepower, and Weight as predictors of the response MPG.

load carsmall
X = [Displacement Horsepower Weight];

Grow a regression tree using the entire data set.

Mdl = fitrtree(X,MPG);

Compute the cross-validation error.

rng(1); % For reproducibility
E = cvloss(Mdl)
E = 
27.6976

E is the 10-fold weighted, average MSE (weighted by number of test observations in the folds).

Open Live Script

Apply k-fold cross validation to find the best level to prune a regression tree for all of its subtrees.

Load the carsmall data set. Consider Displacement, Horsepower, and Weight as predictors of the response MPG.

load carsmall
X = [Displacement Horsepower Weight];

Grow a regression tree using the entire data set. View the resulting tree.

Mdl = fitrtree(X,MPG);
view(Mdl,Mode="graph")

Figure Regression tree viewer contains an axes object and other objects of type uimenu, uicontrol. The axes object contains 60 objects of type line, text. One or more of the lines displays its values using only markers

Compute the 5-fold cross-validation error for each subtree except for the first two lowest and highest pruning level. Specify to return the best pruning level over all subtrees.

rng(1); % For reproducibility
m = max(Mdl.PruneList) - 1
m = 
15

[~,~,~,bestLevel] = cvloss(Mdl,SubTrees=2:m,KFold=5)
bestLevel = 
14

Of the 15 pruning levels, the best pruning level is 14.

Prune the tree to the best level. View the resulting tree.

MdlPrune = prune(Mdl,Level=bestLevel);
view(MdlPrune,Mode="graph")

Figure Regression tree viewer contains an axes object and other objects of type uimenu, uicontrol. The axes object contains 12 objects of type line, text. One or more of the lines displays its values using only markers

Input Arguments

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Regression tree model, specified as a RegressionTree model object trained with fitrtree.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [E,SE,Nleaf,BestLevel] = cvloss(tree,KFold=5) specifies to use 5 cross-validation samples.

Pruning level, specified as a vector of nonnegative integers in ascending order or "all".

If you specify a vector, then all elements must be at least 0 and at most max(tree.PruneList). 0 indicates the full, unpruned tree, and max(tree.PruneList) indicates the completely pruned tree (that is, just the root node).

If you specify "all", then cvloss operates on all subtrees, meaning the entire pruning sequence. This specification is equivalent to using 0:max(tree.PruneList).

cvloss prunes tree to each level specified by Subtrees, and then estimates the corresponding output arguments. The size of Subtrees determines the size of some output arguments.

For the function to invoke Subtrees, the properties PruneList and PruneAlpha of tree must be nonempty. In other words, grow tree by setting Prune="on" when you use fitrtree, or by pruning tree using prune.

Example: Subtrees="all"

Data Types: single | double | char | string

Tree size, specified as one of these values:

  • "se" — cvloss returns the best pruning level (BestLevel), which corresponds to the highest pruning level with the loss within one standard deviation of the minimum (L+se, where L and se relate to the smallest value in Subtrees).

  • "min" — cvloss returns the best pruning level, which corresponds to the element of Subtrees with the smallest loss. This element is usually the smallest element of Subtrees.

Example: TreeSize="min"

Data Types: char | string

Number of cross-validation samples, specified as a positive integer value greater than 1.

Example: KFold=8

Data Types: single | double

Output Arguments

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Cross-validation mean squared error (loss), returned as a numeric vector of the same length as Subtrees.

Standard error of E, returned as a numeric vector of the same length as Subtrees.

Number of leaf nodes in the pruned subtrees, returned as a numeric vector of the same length as Subtrees. Leaf nodes are terminal nodes, which give responses, not splits.

Best pruning level, returned as a numeric scalar whose value depends on TreeSize:

  • When TreeSize is "se", the loss function returns the highest pruning level whose loss is within one standard deviation of the minimum (L+se, where L and se relate to the smallest value in Subtrees).

  • When TreeSize is "min", the loss function returns the element of Subtrees with the smallest loss, usually the smallest element of Subtrees.

Alternatives

You can create a cross-validated tree model using crossval, and call kfoldLoss instead of cvloss. If you are going to examine the cross-validated tree more than once, then the alternative can save time.

However, unlike cvloss, kfoldLoss does not return SE, Nleaf, or BestLevel.

Extended Capabilities

Version History

Introduced in R2011a

See Also

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