resubPredict

Predict resubstitution labels of classification tree

Syntax

label = resubPredict(tree)

[label,posterior] = resubPredict(tree)

[label,posterior,node] = resubPredict(tree)

[label,posterior,node,cnum] = resubPredict(tree)

[label,___] = resubPredict(tree,Name,Value)

Description

label = resubPredict(tree) returns the labels tree predicts for the data tree.X. label is the predictions of tree on the data that fitctree used to create tree.

[label,posterior] = resubPredict(tree) returns the posterior class probabilities for the predictions.

[label,posterior,node] = resubPredict(tree) returns the node numbers of tree for the resubstituted data.

[label,posterior,node,cnum] = resubPredict(tree) returns the predicted class numbers for the predictions.

[label,___] = resubPredict(tree,Name,Value) returns resubstitution predictions with additional options specified by one or more Name,Value pair arguments.

Examples

Compute Number of Misclassified Observations

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

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

ans = 3

Compare In-Sample Posterior Probabilities for Each Subtree

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

load fisheriris

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.

Posterior Probability Definition for Classification Tree

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

tree — Classification tree

ClassificationTree object

Classification tree, specified as a ClassificationTree object. Use the fitctree function to create a classification tree object.

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: [~,posterior] = resubPredict(tree,'SubTrees',[1 3]);

Subtrees — Pruning level

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

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 (i.e., just the root node).

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

resubPredict 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

Output Arguments

label — Response tree predicts for training data

vector | matrix

Response tree predicts for the training data, returned as a vector or matrix. label is the same data type as the training response data tree.Y.

If the Subtrees name-value pair argument 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 — Posterior probabilities for classes tree predicts

matrix | array

Posterior probabilities for classes tree predicts, returned as a matrix or array.

If the Subtrees name-value argument is a scalar or is missing, posterior is an n-by-k 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, posterior is an n-by-k-by-m array, where the matrix for each m gives posterior probabilities for the corresponding subtree.

node — Node numbers of tree where each data row resolves

vector | matrix

Node numbers of tree where each data row resolves, returned as a vector or matrix.

If the Subtrees name-value argument is a scalar or is missing, node is a numeric column vector with n rows, the same number of rows as tree.X.

If Subtrees contains m>1 entries, node is a n-by-m matrix. Each column represents the node predictions of the corresponding subtree.

cnum — Class numbers tree predicts for resubstituted data

vector | matrix

Class numbers that tree predicts for resubstituted data, returned as a vector or matrix.

If the Subtrees name-value argument is a scalar or is missing, cnum is a numeric column vector with n rows, the same number of rows as tree.X.

If Subtrees contains m>1 entries, cnum is a n-by-m matrix. Each column represents the class predictions of the corresponding subtree.

More About

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.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2011a