# resubPredict

Classify observations in classification tree by resubstitution

## Description

example

label = resubPredict(tree) returns the predicted class labels for the trained classification tree model tree using the predictor data stored in tree.X. label has the same data type as the training response data tree.Y.

example

label = resubPredict(tree,Subtrees=subtrees) also prunes tree to the level specified by subtrees.

example

[label,posterior,node,cnum] = resubPredict(tree) also returns the posterior class probabilities, the predicted class numbers, and the node numbers of tree for the resubstituted data, using any of the input arguments in the previous syntaxes.

## Examples

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Find the total number of misclassifications of the Fisher iris data for a classification tree.

tree = fitctree(meas,species);
Ypredict = resubPredict(tree);    % The predictions
Ysame = strcmp(Ypredict,species); % True when ==
sum(~Ysame) % How many are different?
ans = 3

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

Grow a classification tree using the all petal measurements.

Mdl = fitctree(meas(:,3:4),species);
n = size(meas,1); % Sample size
K = numel(Mdl.ClassNames); % Number of classes

View the classification tree.

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

The classification tree has four pruning levels. Level 0 is the full, unpruned tree (as displayed). Level 4 is just the root node (i.e., no splits).

Estimate the posterior probabilities for each class using the subtrees pruned to levels 1 and 3.

[~,Posterior] = resubPredict(Mdl,'Subtrees',[1 3]);

Posterior is an n-by- K-by- 2 array of posterior probabilities. Rows of Posterior correspond to observations, columns correspond to the classes with order Mdl.ClassNames, and pages correspond to pruning level.

Display the class posterior probabilities for iris 125 using each subtree.

Posterior(125,:,:)
ans =
ans(:,:,1) =

0    0.0217    0.9783

ans(:,:,2) =

0    0.5000    0.5000

The decision stump (page 2 of Posterior) has trouble predicting whether iris 125 is versicolor or virginica.

Classify a predictor X as true when X < 0.15 or X > 0.95, and as false otherwise.

Generate 100 uniformly distributed random numbers between 0 and 1, and classify them using a tree model.

rng("default") % For reproducibility
X = rand(100,1);
Y = (abs(X - 0.55) > 0.4);
tree = fitctree(X,Y);
view(tree,"Mode","graph")

Prune the tree.

tree1 = prune(tree,"Level",1);
view(tree1,"Mode","graph")

The pruned tree correctly classifies observations that are less than 0.15 as true. It also correctly classifies observations from 0.15 to 0.95 as false. However, it incorrectly classifies observations that are greater than 0.95 as false. Therefore, the score for observations that are greater than 0.15 should be about 0.05/0.85=0.06 for true, and about 0.8/0.85=0.94 for false.

Compute the prediction scores (posterior probabilities) for the first 10 rows of X.

[~,score] = resubPredict(tree1);
[score(1:10,:) X(1:10)]
ans = 10×3

0.9059    0.0941    0.8147
0.9059    0.0941    0.9058
0    1.0000    0.1270
0.9059    0.0941    0.9134
0.9059    0.0941    0.6324
0    1.0000    0.0975
0.9059    0.0941    0.2785
0.9059    0.0941    0.5469
0.9059    0.0941    0.9575
0.9059    0.0941    0.9649

Indeed, every value of X (the right-most column) that is less than 0.15 has associated scores (the left and center columns) of 0 and 1, while the other values of X have associated scores of approximately 0.91 and 0.09. The difference (score of 0.09 instead of the expected 0.06) is due to a statistical fluctuation: there are 8 observations in X in the range (0.95,1) instead of the expected 5 observations.

sum(X > 0.95)
ans = 8

## Input Arguments

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

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 resubPredict operates on all subtrees (that is, the entire pruning sequence). This specification is equivalent to using 0:max(tree.PruneList).

resubPredict 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.

Data Types: single | double | char | string

## Output Arguments

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Predicted class labels for the training data, returned as a categorical or character array, logical or numeric vector, or cell array of character vectors. label has the same data type as the training response data tree.Y.

If subtrees contains m > 1 entries, then label is returned as a matrix with m columns, each of which represents the predictions of the corresponding subtree. Otherwise, label is returned as a vector.

Posterior probabilities for the classes predicted by tree, returned as a numeric matrix or numeric array.

If subtrees is a scalar or is not specified, then resubPredict returns posterior as an n-by-k numeric matrix, where n is the number of rows in the training data tree.X, and k is the number of classes.

If subtrees contains m > 1 entries, then resubPredict returns posterior as an n-by-k-by-m numeric array, where the matrix for each m gives posterior probabilities for the corresponding subtree.

Node numbers for the predicted classes, returned as a numeric column vector or numeric matrix.

If subtrees is a scalar or is not specified, then resubPredict returns node as a numeric column vector with n rows, the same number of rows as tree.X.

If subtrees contains m > 1 entries, then node is an n-by-m numeric matrix. Each column represents the node predictions of the corresponding subtree.

Predicted class numbers for resubstituted data, returned as a numeric column vector or numeric matrix.

If subtrees is a scalar or is not specified, then cnum is a numeric column vector with n rows, the same number of rows as tree.X.

If subtrees contains m > 1 entries, then cnum is an n-by-m numeric matrix. Each column represents the class predictions of the corresponding subtree.

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### Posterior Probability

The posterior probability of the classification at a node is the number of training sequences that lead to that node with this classification, divided by the number of training sequences that lead to that node.

For an example, see Posterior Probability Definition for Classification Tree.

## Version History

Introduced in R2011a