cvloss

Class: ClassificationTree

Classification error by cross validation

Syntax

E = cvloss(tree)

[E,SE] = cvloss(tree)

[E,SE,Nleaf] = cvloss(tree)

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

[___] = cvloss(tree,Name,Value)

Description

E = cvloss(tree) returns the cross-validated classification error (loss) for tree, a classification tree. The cvloss method uses stratified partitioning to create cross-validated sets. That is, for each fold, each partition of the data has roughly the same class proportions as in the data used to train tree.

[E,SE] = cvloss(tree) returns the standard error of E.

[E,SE,Nleaf] = cvloss(tree) returns the number of leaves of tree.

[E,SE,Nleaf,BestLevel] = cvloss(tree) returns the optimal pruning level for tree.

[___] = cvloss(tree,Name,Value) cross validates with additional options specified by one or more Name,Value pair arguments, using any of the previous syntaxes. You can specify several name-value pair arguments in any order as Name1,Value1,…,NameN,ValueN.

Input Arguments

tree — Trained classification tree

ClassificationTree model object

Trained classification tree, specified as a ClassificationTree model object produced by fitctree.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'Subtrees' — Pruning level

0 (default) | vector of nonnegative integers | 'all'

Pruning level, specified as the comma-separated pair consisting of 'Subtrees' and 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 (i.e., just the root node).

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

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

To invoke Subtrees, the properties PruneList and PruneAlpha of tree must be nonempty. In other words, grow tree by setting 'Prune','on', or by pruning tree using prune.

Example: 'Subtrees','all'

Data Types: single | double | char | string

'TreeSize' — Tree size

'se' (default) | 'min'

Tree size, specified as the comma-separated pair consisting of 'TreeSize' and one of the following values:

• 'se' — cvloss uses the smallest tree whose cost is within one standard error of the minimum cost.

• 'min' — cvloss uses the minimal cost tree.

Example: 'TreeSize','min'

'KFold' — Number of cross-validation samples

10 (default) | positive integer value greater than 1

Number of cross-validation samples, specified as the comma-separated pair consisting of KFold and a positive integer value greater than 1.

Example: 'KFold',8

Output Arguments

E — Cross-validation classification error

numeric vector | scalar value

Cross-validation classification error (loss), returned as a vector or scalar depending on the setting of the Subtrees name-value pair.

SE — Standard error

numeric vector | scalar value

Standard error of E, returned as a vector or scalar depending on the setting of the Subtrees name-value pair.

Nleaf — Number of leaf nodes

numeric vector | scalar value

Number of leaf nodes in tree, returned as a vector or scalar depending on the setting of the Subtrees name-value pair. Leaf nodes are terminal nodes, which give classifications, not splits.

BestLevel — Best pruning level

scalar value

Best pruning level, returned as a scalar value. By default, a scalar representing the largest pruning level that achieves a value of E within SE of the minimum error. If you set TreeSize to 'min', BestLevel is the smallest value in Subtrees.

Examples

Compute the Cross-Validation Error

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

Load the ionosphere data set.

load ionosphere

Grow a classification tree using the entire data set.

Mdl = fitctree(X,Y);

Compute the cross-validation error.

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

E = 0.1111

E is the 10-fold misclassification error.

Find the Best Pruning Level Using Cross Validation

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

Load the ionosphere data set.

load ionosphere

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

Mdl = fitctree(X,Y);
view(Mdl,'Mode','graph')

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

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

m = 7

[E,~,~,bestLevel] = cvloss(Mdl,'SubTrees',0:m,'KFold',5)

E = 8×1

    0.1368
    0.1339
    0.1311
    0.1339
    0.1339
    0.1254
    0.0997
    0.1738

bestLevel = 6

Of the 7 pruning levels, the best pruning level is 6.

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

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

Alternatives

You can construct a cross-validated tree model with 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. kfoldLoss also does not allow you to examine any error other than the classification error.