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resubLoss

Resubstitution classification loss for classification tree model

Description

L = resubLoss(tree) returns the classification loss L by resubstitution for the trained classification tree model tree using the training data stored in tree.X and the corresponding true class labels stored in tree.Y. By default, resubLoss uses the loss computed for the data used by fitctree to create tree.

The classification loss (L) is a resubstitution quality measure. Its interpretation depends on the loss function (LossFun), but in general, better classifiers yield smaller classification loss values. The default LossFun value is "mincost" (minimal expected misclassification cost).

example

L = resubLoss(tree,Name=Value) specifies additional options using one or more name-value arguments. For example, you can specify the loss function, pruning level, and the tree size that resubLoss uses to calculate the classification loss.

example

[L,SE,Nleaf,BestLevel] = resubLoss(___) also returns the standard errors of the classification errors, the number of leaf nodes in the trees of the pruning sequence, and the best pruning level as defined in the TreeSize name-value argument. By default, BestLevel is the pruning level that gives loss within one standard deviation of the minimal loss.

Examples

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Compute the resubstitution classification error for the ionosphere data.

load ionosphere
tree = fitctree(X,Y);
L = resubLoss(tree)
L = 
0.0114

Unpruned decision trees tend to overfit. One way to balance model complexity and out-of-sample performance is to prune a tree (or restrict its growth) so that in-sample and out-of-sample performance are satisfactory.

Load Fisher's iris data set. Partition the data into training (50%) and validation (50%) sets.

load fisheriris
n = size(meas,1);
rng(1) % For reproducibility
idxTrn = false(n,1);
idxTrn(randsample(n,round(0.5*n))) = true; % Training set logical indices 
idxVal = idxTrn == false;                  % Validation set logical indices

Grow a classification tree using the training set.

Mdl = fitctree(meas(idxTrn,:),species(idxTrn));

View the classification tree.

view(Mdl,'Mode','graph');

Figure Classification tree viewer contains an axes object and other objects of type uimenu, uicontrol. The axes object contains 18 objects of type line, text. One or more of the lines displays its values using only markers

The classification tree has four pruning levels. Level 0 is the full, unpruned tree (as displayed). Level 3 is just the root node (i.e., no splits).

Examine the training sample classification error for each subtree (or pruning level) excluding the highest level.

m = max(Mdl.PruneList) - 1;
trnLoss = resubLoss(Mdl,'Subtrees',0:m)
trnLoss = 3×1

    0.0267
    0.0533
    0.3067

  • The full, unpruned tree misclassifies about 2.7% of the training observations.

  • The tree pruned to level 1 misclassifies about 5.3% of the training observations.

  • The tree pruned to level 2 (i.e., a stump) misclassifies about 30.6% of the training observations.

Examine the validation sample classification error at each level excluding the highest level.

valLoss = loss(Mdl,meas(idxVal,:),species(idxVal),'Subtrees',0:m)
valLoss = 3×1

    0.0369
    0.0237
    0.3067

  • The full, unpruned tree misclassifies about 3.7% of the validation observations.

  • The tree pruned to level 1 misclassifies about 2.4% of the validation observations.

  • The tree pruned to level 2 (i.e., a stump) misclassifies about 30.7% of the validation observations.

To balance model complexity and out-of-sample performance, consider pruning Mdl to level 1.

pruneMdl = prune(Mdl,'Level',1);
view(pruneMdl,'Mode','graph')

Figure Classification 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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Classification tree model, specified as a ClassificationTree model object trained with fitctree.

Name-Value Arguments

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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: L = resubLoss(tree,Subtrees="all") specifies to use all subtrees when computing the resubstitution classification loss for tree.

Loss function, specified as a built-in loss function name or a function handle.

The following table describes the values for the built-in loss functions.

ValueDescription
"binodeviance"Binomial deviance
"classifcost"Observed misclassification cost
"classiferror"Misclassified rate in decimal
"exponential"Exponential loss
"hinge"Hinge loss
"logit"Logistic loss
"mincost"Minimal expected misclassification cost (for classification scores that are posterior probabilities)
"quadratic"Quadratic loss

"mincost" is appropriate for classification scores that are posterior probabilities. Classification trees return posterior probabilities as classification scores by default (see predict).

Specify your own function using function handle notation. Suppose that n is the number of observations in X, and K is the number of distinct classes (numel(tree.ClassNames)). Your function must have the signature

lossvalue = lossfun(C,S,W,Cost)
where:

  • The output argument lossvalue is a scalar.

  • You specify the function name (lossfun).

  • C is an n-by-K logical matrix with rows indicating the class to which the corresponding observation belongs. The column order corresponds to the class order in tree.ClassNames.

    Create C by setting C(p,q) = 1, if observation p is in class q, for each row. Set all other elements of row p to 0.

  • S is an n-by-K numeric matrix of classification scores. The column order corresponds to the class order in tree.ClassNames. S is a matrix of classification scores, similar to the output of predict.

  • W is an n-by-1 numeric vector of observation weights. If you pass W, the software normalizes the weights to sum to 1.

  • Cost is a K-by-K numeric matrix of misclassification costs. For example, Cost = ones(K) - eye(K) specifies a cost of 0 for correct classification and 1 for misclassification.

For more details on loss functions, see Classification Loss.

Example: LossFun="binodeviance"

Example: LossFun=@lossfun

Data Types: char | string | function_handle

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 resubLoss operates on all subtrees (in other words, the entire pruning sequence). This specification is equivalent to using 0:max(tree.PruneList).

resubLoss 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 fitctree, or by pruning tree using prune.

Example: Subtrees="all"

Data Types: single | double | char | string

Tree size, specified as one of these values:

  • "se"resubLoss 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"resubLoss 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

Output Arguments

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Classification loss, returned as a vector of scalar values that has the same length as Subtrees. The meaning of the error depends on the loss function (LossFun).

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

Number of leaf nodes in the pruned subtrees, returned as a vector of integer values that has 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.

More About

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Extended Capabilities

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Version History

Introduced in R2011a