Predict resubstitution labels of classification tree
label = resubPredict(tree)
[label,posterior] = resubPredict(tree)
[label,posterior,node] = resubPredict(tree)
[label,posterior,node,cnum] = resubPredict(tree)
[label,...] = resubPredict(tree,Name,Value)
A classification tree constructed by
Specify optional pairs of arguments as
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.
Matrix or array of posterior probabilities for classes
The node numbers of
The class numbers that
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%)
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.
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
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.
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
Compute the prediction scores (posterior probabilities) for the first 10 rows of
[~,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
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.
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).